Find all School-related info fast with the new School-Specific MBA Forum

It is currently 21 Oct 2014, 03:23

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If angle BAD is a right angle, what is the length of side

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Intern
Intern
avatar
Joined: 12 Aug 2010
Posts: 14
Followers: 0

Kudos [?]: 7 [1] , given: 0

If angle BAD is a right angle, what is the length of side [#permalink] New post 30 Nov 2010, 10:09
1
This post received
KUDOS
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

54% (02:04) correct 46% (00:53) wrong based on 226 sessions
Image
If angle BAD is a right angle, what is the length of side BD?

(1) AC is perpendicular to BD

(2) BC = CD

[Reveal] Spoiler:
Official answer explanation:

Using statements 1 and 2, we know that AC is the perpendicular bisector of BD. This means that triangle BAD is an isosceles triangle so side AB must have a length of 5 (the same length as side AD). We also know that angle BAD is a right angle, so side BD is the hypotenuse of right isosceles triangle BAD. If each leg of the triangle is 5, the hypotenuse (using the Pythagorean theorem) must be 5 underroot 2.

Can someone kindly explainthe underlined portion?
[Reveal] Spoiler: OA

Last edited by Bunuel on 16 Jun 2013, 22:53, edited 1 time in total.
Edited the question and the OA.
Kaplan Promo CodeKnewton GMAT Discount CodesGMAT Pill GMAT Discount Codes
Expert Post
5 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23351
Followers: 3602

Kudos [?]: 28699 [5] , given: 2809

Re: isosceles triangle property [#permalink] New post 30 Nov 2010, 10:41
5
This post received
KUDOS
Expert's post
chiragatara wrote:
If angle BAD is a right angle, what is the length of side BD?

(1) AC is perpendicular to BD

(2) BC = CD

Official answer explanation:

Using statements 1 and 2, we know that AC is the perpendicular bisector of BD. This means that triangle BAD is an isosceles triangle so side AB must have a length of 5 (the same length as side AD). We also know that angle BAD is a right angle, so side BD is the hypotenuse of right isosceles triangle BAD. If each leg of the triangle is 5, the hypotenuse (using the Pythagorean theorem) must be 5 underroot 2.

Can someone kindly explainthe underlined portion?


For such kind of graphic questions you MUST post the image. Next, please also do check the OA's when posting a question, OA for this one is C, not E.

Original question is below:

If angle BAD is a right angle, what is the length of side BD?
Attachment:
triangleABCD.jpg
triangleABCD.jpg [ 23.6 KiB | Viewed 4354 times ]

(1) AC is perpendicular to BD
(2) BC = CD

Now, obviously each statement alone is not sufficient.

When taken together we have that AC is a perpendicular bisector. Now, if a line from a vertex to the opposite side is both perpendicular to it and bisects it then this side is a base of an isosceles triangle (or in other words if a bisector and perpendicular coincide then we have an isosceles triangle). You can check this yourself: in triangles ACD and ACB two sides are equal (AC=AC and BC=CD) and included angle between these sides are also equal (<ACD=<ACB=90) so we have Side-Angle-Side case (SAS), which means that ACD and ACB are congruent triangles, so AB=AD --> ABD is an isosceles triangle.

Next, as ABD is an isosceles triangle then AB=AD=5 and hypotenuse BD=5\sqrt{2}.

Answer: C.

For more on this Triangles chapter of Math Book: math-triangles-87197.html

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 12 Oct 2011
Posts: 133
GMAT 1: 700 Q48 V37
GMAT 2: 720 Q48 V40
Followers: 3

Kudos [?]: 66 [0], given: 23

Re: If angle BAD is a right angle, what is the length of side [#permalink] New post 19 Oct 2012, 12:24
If AC is perpendicular to BD, then AC is the altitude from the right angle, isn't it? That would imply that triangles ABC and ACD are similar, so that angle CDA is equal to angle ABC, thus making triangle ABD an isoeleces right triangle and you could calculate BD then. What is wrong with that argumentation?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23351
Followers: 3602

Kudos [?]: 28699 [0], given: 2809

Re: If angle BAD is a right angle, what is the length of side [#permalink] New post 23 Oct 2012, 06:19
Expert's post
BN1989 wrote:
If AC is perpendicular to BD, then AC is the altitude from the right angle, isn't it? That would imply that triangles ABC and ACD are similar, so that angle CDA is equal to angle ABC, thus making triangle ABD an isoeleces right triangle and you could calculate BD then. What is wrong with that argumentation?


Yes, the perpendicular to the hypotenuse will always divide the triangle into two triangles with the same properties as the original triangle. But the corresponding (equal) angles would be BAC and ADC (also DAC and ABC) not CDA and ABC.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 22 Oct 2012
Posts: 20
Followers: 0

Kudos [?]: 1 [0], given: 7

GMAT ToolKit User
Re: If angle BAD is a right angle, what is the length of side [#permalink] New post 25 Nov 2012, 23:14
Bunuel wrote:
BN1989 wrote:
If AC is perpendicular to BD, then AC is the altitude from the right angle, isn't it? That would imply that triangles ABC and ACD are similar, so that angle CDA is equal to angle ABC, thus making triangle ABD an isoeleces right triangle and you could calculate BD then. What is wrong with that argumentation?


Yes, the perpendicular to the hypotenuse will always divide the triangle into two triangles with the same properties as the original triangle. But the corresponding (equal) angles would be BAC and ADC (also DAC and ABC) not CDA and ABC.

Hope it's clear.


Bunuel, hi,

Where in the question it is mentionned that a side is equal to 5?
Without any value, it s E...

Thank you to make a clarification.

Kind Regards,

R26

Image Posted from GMAT ToolKit
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23351
Followers: 3602

Kudos [?]: 28699 [0], given: 2809

Re: If angle BAD is a right angle, what is the length of side [#permalink] New post 26 Nov 2012, 01:23
Expert's post
R26 wrote:
Bunuel wrote:
BN1989 wrote:
If AC is perpendicular to BD, then AC is the altitude from the right angle, isn't it? That would imply that triangles ABC and ACD are similar, so that angle CDA is equal to angle ABC, thus making triangle ABD an isoeleces right triangle and you could calculate BD then. What is wrong with that argumentation?


Yes, the perpendicular to the hypotenuse will always divide the triangle into two triangles with the same properties as the original triangle. But the corresponding (equal) angles would be BAC and ADC (also DAC and ABC) not CDA and ABC.

Hope it's clear.


Bunuel, hi,

Where in the question it is mentionned that a side is equal to 5?
Without any value, it s E...

Thank you to make a clarification.

Kind Regards,

R26

Image Posted from GMAT ToolKit


Please read this post: if-angle-bad-is-a-right-angle-what-is-the-length-of-side-105559.html#p825162

Diagram attached to the original question shows that AD=5.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 22 Oct 2012
Posts: 20
Followers: 0

Kudos [?]: 1 [0], given: 7

GMAT ToolKit User
Re: If angle BAD is a right angle, what is the length of side [#permalink] New post 26 Nov 2012, 01:29
Ah I see.
The diagram is not coming out when the questions are sync with the app. I ll tell walker then to add it for the update!
Thank you!
Manager
Manager
avatar
Joined: 09 May 2013
Posts: 57
Followers: 0

Kudos [?]: 8 [0], given: 12

Re: If angle BAD is a right angle, what is the length of side [#permalink] New post 21 Jun 2013, 07:45
Bunuel wrote:
BN1989 wrote:
If AC is perpendicular to BD, then AC is the altitude from the right angle, isn't it? That would imply that triangles ABC and ACD are similar, so that angle CDA is equal to angle ABC, thus making triangle ABD an isoeleces right triangle and you could calculate BD then. What is wrong with that argumentation?


Yes, the perpendicular to the hypotenuse will always divide the triangle into two triangles with the same properties as the original triangle. But the corresponding (equal) angles would be BAC and ADC (also DAC and ABC) not CDA and ABC.

Hope it's clear.


i dint understood these part bunuel
how to find corresponding angles of similar triangles?
Manager
Manager
avatar
Status: Trying.... & desperate for success.
Joined: 17 May 2012
Posts: 79
Location: India
Concentration: Leadership, Entrepreneurship
Schools: NUS '15
GMAT 1: Q33 V27
GPA: 2.92
WE: Analyst (Computer Software)
Followers: 0

Kudos [?]: 25 [0], given: 61

Re: If angle BAD is a right angle, what is the length of side [#permalink] New post 22 Jun 2013, 05:45
WarriorGmat wrote:
Bunuel wrote:
BN1989 wrote:
If AC is perpendicular to BD, then AC is the altitude from the right angle, isn't it? That would imply that triangles ABC and ACD are similar, so that angle CDA is equal to angle ABC, thus making triangle ABD an isoeleces right triangle and you could calculate BD then. What is wrong with that argumentation?


Yes, the perpendicular to the hypotenuse will always divide the triangle into two triangles with the same properties as the original triangle. But the corresponding (equal) angles would be BAC and ADC (also DAC and ABC) not CDA and ABC.

Hope it's clear.


i dint understood these part bunuel
how to find corresponding angles of similar triangles?

http://www.mathsteacher.com.au/year9/ch ... imilar.htm

try this site. Also, kindly refer Manhattan's foundation to GMAT math. It will be helpful to strengthen concepts frequently tested on GMAT.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23351
Followers: 3602

Kudos [?]: 28699 [0], given: 2809

Re: If angle BAD is a right angle, what is the length of side [#permalink] New post 22 Jun 2013, 10:26
Expert's post
WarriorGmat wrote:
Bunuel wrote:
BN1989 wrote:
If AC is perpendicular to BD, then AC is the altitude from the right angle, isn't it? That would imply that triangles ABC and ACD are similar, so that angle CDA is equal to angle ABC, thus making triangle ABD an isoeleces right triangle and you could calculate BD then. What is wrong with that argumentation?


Yes, the perpendicular to the hypotenuse will always divide the triangle into two triangles with the same properties as the original triangle. But the corresponding (equal) angles would be BAC and ADC (also DAC and ABC) not CDA and ABC.

Hope it's clear.


i dint understood these part bunuel
how to find corresponding angles of similar triangles?


Check here: similart-triangles-help-from-bunnel-needed-144589.html#p1160271

Hope it heps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Current Student
avatar
Joined: 26 Sep 2013
Posts: 232
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Followers: 2

Kudos [?]: 39 [0], given: 40

Re: If angle BAD is a right angle, what is the length of side [#permalink] New post 21 Oct 2013, 08:20
Bunuel wrote:
BN1989 wrote:
If AC is perpendicular to BD, then AC is the altitude from the right angle, isn't it? That would imply that triangles ABC and ACD are similar, so that angle CDA is equal to angle ABC, thus making triangle ABD an isoeleces right triangle and you could calculate BD then. What is wrong with that argumentation?


Yes, the perpendicular to the hypotenuse will always divide the triangle into two triangles with the same properties as the original triangle. But the corresponding (equal) angles would be BAC and ADC (also DAC and ABC) not CDA and ABC.

Hope it's clear.





Here's what I did, is my logic correct?


(1) AC is perpendicular to BD - you don't know the relationship between bc & cd though - insuff

(2) BC = CD - doesn't tell you anything, because you can't calculate what either length is.

combined: ACD is a 45-45-90, we know the hypotaneuse, and since the sides of a 45-45-90 are in the ratio of 1:1:\sqrt{2}, we can solve for cd, and thus bc. So in this case, with the hypotaneuse being 5, ac & cd are both 5/\sqrt{2}, and since bc=cd, we can solve, thus suff.
Senior Manager
Senior Manager
User avatar
Joined: 13 May 2013
Posts: 476
Followers: 1

Kudos [?]: 58 [0], given: 134

Re: If angle BAD is a right angle, what is the length of side [#permalink] New post 11 Dec 2013, 09:16
If angle BAD is a right angle, what is the length of side BD?

I had originally said B, thinking that because we knew CA was a bisector and that angle A was 90 degrees, there would only be one possible way to configure this triangle. Obviously, this is incorrect. You could have an isosceles triangle or you could have a triangle with a low, long line BA and a relatively short and steep line AD with B as a 90 degree angle.

(1) AC is perpendicular to BD

This tells us that AC is the altitude but little more. Insufficient

(2) BC = CD

This tells us that AC is the bisector. Triangle BAC and DAC have the same area but they could have different exterior measures for BA and DA. Insufficient.

1+2) A line drawn from a vertex to the opposite line that is both perpendicular to that line and bisects it must create a isosceles triangle with that line as the base. This means, BA = AD = 5. Furthermore, BC = CD and they can have exactly one measure...Sufficient.

C
Intern
Intern
avatar
Joined: 05 Feb 2014
Posts: 11
Followers: 0

Kudos [?]: 3 [0], given: 22

GMAT ToolKit User
Re: If angle BAD is a right angle, what is the length of side [#permalink] New post 19 Jul 2014, 06:17
First, I have to say geometry is my weakest area. So be kind to me. :wink:

I don't see why A is wrong. I mean if AC is perpendicular to BD, isn't angle ACD 90° and angle CAD 45° and triangle ACD therefore a 45-45-90 triangle?

I also don't understand why you guys infer from the 2nd statement that triangle ACD is a 45-45-90 triangle.

Can somebody help me with this.
Manager
Manager
avatar
Joined: 10 Mar 2014
Posts: 106
Followers: 1

Kudos [?]: 18 [0], given: 6

CAT Tests
If angle BAD is a right angle, what is the length of side [#permalink] New post 31 Jul 2014, 09:21
Bunuel wrote:
chiragatara wrote:
If angle BAD is a right angle, what is the length of side BD?

(1) AC is perpendicular to BD

(2) BC = CD

Official answer explanation:

Using statements 1 and 2, we know that AC is the perpendicular bisector of BD. This means that triangle BAD is an isosceles triangle so side AB must have a length of 5 (the same length as side AD). We also know that angle BAD is a right angle, so side BD is the hypotenuse of right isosceles triangle BAD. If each leg of the triangle is 5, the hypotenuse (using the Pythagorean theorem) must be 5 underroot 2.

Can someone kindly explainthe underlined portion?


For such kind of graphic questions you MUST post the image. Next, please also do check the OA's when posting a question, OA for this one is C, not E.

Original question is below:

If angle BAD is a right angle, what is the length of side BD?
Image
(1) AC is perpendicular to BD
(2) BC = CD

Now, obviously each statement alone is not sufficient.

When taken together we have that AC is a perpendicular bisector. Now, if a line from a vertex to the opposite side is both perpendicular to it and bisects it then this side is a base of an isosceles triangle (or in other words if a bisector and perpendicular coincide then we have an isosceles triangle). You can check this yourself: in triangles ACD and ACB two sides are equal (AC=AC and BC=CD) and included angle between these sides are also equal (<ACD=<ACB=90) so we have Side-Angle-Side case (SAS), which means that ACD and ACB are congruent triangles, so AB=AD --> ABD is an isosceles triangle.

Next, as ABD is an isosceles triangle then AB=AD=5 and hypotenuse BD=5\sqrt{2}.

Answer: C.

For more on this Triangles chapter of Math Book: math-triangles-87197.html

Hope it helps.


HI Bunuel,

similar kind of question is mentioned on

in-triangle-abc-to-the-right-if-bc-3-and-ac-4-then-88061.html

on above link you have mentioned
perpendicular to the hypotenuse will always divide the triangle into two triangles with the same properties as the original triangle.

what you mean by perpendicular to the hypotenuse

and in this question you are saying that it is an isoceles triangle. by using st1 then why this is not sufficient.

Thanks
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23351
Followers: 3602

Kudos [?]: 28699 [0], given: 2809

Re: If angle BAD is a right angle, what is the length of side [#permalink] New post 31 Jul 2014, 10:01
Expert's post
PathFinder007 wrote:
Bunuel wrote:
chiragatara wrote:
If angle BAD is a right angle, what is the length of side BD?

(1) AC is perpendicular to BD

(2) BC = CD

Official answer explanation:

Using statements 1 and 2, we know that AC is the perpendicular bisector of BD. This means that triangle BAD is an isosceles triangle so side AB must have a length of 5 (the same length as side AD). We also know that angle BAD is a right angle, so side BD is the hypotenuse of right isosceles triangle BAD. If each leg of the triangle is 5, the hypotenuse (using the Pythagorean theorem) must be 5 underroot 2.

Can someone kindly explainthe underlined portion?


For such kind of graphic questions you MUST post the image. Next, please also do check the OA's when posting a question, OA for this one is C, not E.

Original question is below:

If angle BAD is a right angle, what is the length of side BD?
Image
(1) AC is perpendicular to BD
(2) BC = CD

Now, obviously each statement alone is not sufficient.

When taken together we have that AC is a perpendicular bisector. Now, if a line from a vertex to the opposite side is both perpendicular to it and bisects it then this side is a base of an isosceles triangle (or in other words if a bisector and perpendicular coincide then we have an isosceles triangle). You can check this yourself: in triangles ACD and ACB two sides are equal (AC=AC and BC=CD) and included angle between these sides are also equal (<ACD=<ACB=90) so we have Side-Angle-Side case (SAS), which means that ACD and ACB are congruent triangles, so AB=AD --> ABD is an isosceles triangle.

Next, as ABD is an isosceles triangle then AB=AD=5 and hypotenuse BD=5\sqrt{2}.

Answer: C.

For more on this Triangles chapter of Math Book: math-triangles-87197.html

Hope it helps.


HI Bunuel,

similar kind of question is mentioned on

in-triangle-abc-to-the-right-if-bc-3-and-ac-4-then-88061.html

on above link you have mentioned
perpendicular to the hypotenuse will always divide the triangle into two triangles with the same properties as the original triangle.

what you mean by perpendicular to the hypotenuse

and in this question you are saying that it is an isoceles triangle. by using st1 then why this is not sufficient.

Thanks


Perpendicular to hypotenuse is a perpendicular from A to BD.

As for why the first statement is not sufficient. All we know that one of the legs is 5, nothing else. HOW are you going to find BD? BD could take ANY length.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 10 Mar 2014
Posts: 106
Followers: 1

Kudos [?]: 18 [0], given: 6

CAT Tests
Re: If angle BAD is a right angle, what is the length of side [#permalink] New post 31 Jul 2014, 11:58
Bunuel wrote:
chiragatara wrote:
If angle BAD is a right angle, what is the length of side BD?

(1) AC is perpendicular to BD

(2) BC = CD

Official answer explanation:

Using statements 1 and 2, we know that AC is the perpendicular bisector of BD. This means that triangle BAD is an isosceles triangle so side AB must have a length of 5 (the same length as side AD). We also know that angle BAD is a right angle, so side BD is the hypotenuse of right isosceles triangle BAD. If each leg of the triangle is 5, the hypotenuse (using the Pythagorean theorem) must be 5 underroot 2.

Can someone kindly explainthe underlined portion?


For such kind of graphic questions you MUST post the image. Next, please also do check the OA's when posting a question, OA for this one is C, not E.

Original question is below:

If angle BAD is a right angle, what is the length of side BD?
Attachment:
triangleABCD.jpg

(1) AC is perpendicular to BD
(2) BC = CD

Now, obviously each statement alone is not sufficient.

When taken together we have that AC is a perpendicular bisector. Now, if a line from a vertex to the opposite side is both perpendicular to it and bisects it then this side is a base of an isosceles triangle (or in other words if a bisector and perpendicular coincide then we have an isosceles triangle). You can check this yourself: in triangles ACD and ACB two sides are equal (AC=AC and BC=CD) and included angle between these sides are also equal (<ACD=<ACB=90) so we have Side-Angle-Side case (SAS), which means that ACD and ACB are congruent triangles, so AB=AD --> ABD is an isosceles triangle.

Next, as ABD is an isosceles triangle then AB=AD=5 and hypotenuse BD=5\sqrt{2}.

Answer: C.

For more on this Triangles chapter of Math Book: math-triangles-87197.html

Hope it helps.


HI Bunuel,

I am getting confusion with following statement

or in other words if a bisector and perpendicular coincide then we have an isosceles triangle)

so if i use this statement and it is given that BAD = 90 then angle b and d would be 45 and i can get BD = 5 root 2.

Please clarify

Thanks.
Re: If angle BAD is a right angle, what is the length of side   [#permalink] 31 Jul 2014, 11:58
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic AD = BD = CD. If angle BAD = 50°, what is angle BCA? awal_786@hotmail.com 2 02 Jun 2014, 15:21
1 Experts publish their posts in the topic Ratio between angles and sides in a right angle traingle. nkimidi7y 11 02 May 2012, 08:32
1 Experts publish their posts in the topic If angle BAD is a right angle, what is the length of side gottabwise 5 23 Jan 2010, 15:43
There is a right angle triangle three side p, n, s, what's ipc302 6 12 Feb 2006, 19:21
Display posts from previous: Sort by

If angle BAD is a right angle, what is the length of side

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.