It is currently 13 Dec 2017, 03:27

Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1


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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The perimeter of a certain isosceles right triangle is 16 +

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 24 Feb 2011
Posts: 29

Kudos [?]: 23 [0], given: 1

Re: The perimeter of a certain isosceles right triangle is 16 + [#permalink]

Show Tags

New post 03 Aug 2011, 13:02
Baten80 had the best answer!!
No one before him mentioned that "This problem can be solved using 45:45:90 isosceles triangle rule. As per properties of 45:45:90 triangle, the sides are in the ratio of 1:1: √2"
Here i was, wondering why everyone takes a sqr of x in their answers. Thank you!

Kudos [?]: 23 [0], given: 1

Intern
Intern
avatar
Joined: 04 Jun 2011
Posts: 34

Kudos [?]: 65 [0], given: 61

Re: The perimeter of a certain isosceles right triangle is 16 + [#permalink]

Show Tags

New post 21 Aug 2011, 17:57
Please explain these 3 steps - I'm not getting the Algebra. I'm sorry to be a pest:

x(2+sqrt2) = 16(1+sqrt2) ( I understand how you got here....but these next step loses me)

x(sqrt2*sqrt2 + sqrt2) = 16(1+sqrt2) ??????

x(sqrt2)(sqrt2 +1) = 16(1 + sqrt2) Cancel out the (1+sqrt2)

x(sqrt2) = 16 = Hypotenuse


Thanks!!!!

Kudos [?]: 65 [0], given: 61

Senior Manager
Senior Manager
avatar
Joined: 13 May 2011
Posts: 292

Kudos [?]: 294 [0], given: 11

WE 1: IT 1 Yr
WE 2: Supply Chain 5 Yrs
Re: The perimeter of a certain isosceles right triangle is 16 + [#permalink]

Show Tags

New post 10 Oct 2011, 03:43
1. a+2b=16(1+root2)
2. b=a/root2

solving for a in 1: a=16

PS: Sorry for the earlier mistake.

Last edited by BDSunDevil on 10 Oct 2011, 04:10, edited 2 times in total.

Kudos [?]: 294 [0], given: 11

Intern
Intern
avatar
Joined: 13 Jul 2010
Posts: 17

Kudos [?]: 2 [0], given: 25

Re: The perimeter of a certain isosceles right triangle is 16 + [#permalink]

Show Tags

New post 28 Sep 2013, 11:12
coffeeloverfreak wrote:
The perimeter of a certain isosceles right triangle is \(16 + 16 \sqrt{2}\). What is the length of the hypotenuse of the triangle?

\((A) \hspace{5} 8\)
\((B) \hspace{5} 16\)
\((C) \hspace{5} 4\sqrt{2}\)
\((D) \hspace{5} 8\sqrt{2}\)
\((E) \hspace{5} 16\sqrt{2}\)


I think the the best approach here is Ballparking the size of the Hypotenuse and POE:

We know that the perimeter is 16+16*root(2)=16+ (about 27 since (16^2=256))= a little more than 42. 42/3=14, so each side is about 13 and the Hypotenuse is 13*1.7=about 15 - closest answer choice is B.

Kudos [?]: 2 [0], given: 25

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14877

Kudos [?]: 287 [0], given: 0

Premium Member
Re: The perimeter of a certain isosceles right triangle is 16 + [#permalink]

Show Tags

New post 28 Sep 2014, 11:48
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 287 [0], given: 0

Intern
Intern
avatar
Joined: 10 Dec 2014
Posts: 37

Kudos [?]: 6 [0], given: 5

GMAT Date: 12-30-2014
Re: The perimeter of a certain isosceles right triangle is 16 + [#permalink]

Show Tags

New post 17 Dec 2014, 03:50
Let the hypotenuse be a.
Then the sides are a/sqrt(2). Sum of the 2 sides = 2*a/sqrt(2) = a*sqrt (2)

So the equation becomes a+a*sqrt(2) = 16+16*sqrt(2)==>t a = 16.

Kudos [?]: 6 [0], given: 5

Intern
Intern
User avatar
Joined: 21 Apr 2014
Posts: 40

Kudos [?]: 27 [0], given: 0

Re: The perimeter of a certain isosceles right triangle is 16 + [#permalink]

Show Tags

New post 07 Mar 2015, 18:36
So we know that the proportions of a isosceles right triangle are x:x:x\sqrt{2}, since the perimeter is 16+16*sqrt(2), then
2x+x*sqrt(2)=16+16\sqrt{2}. we can solve for x and use that information to figure out what the hypotenuse is

First, let's isolate x, so we get x=16+16*sqrt(2)/(2+sqrt(2))
we can eliminate the root from the denominator by multiplying both the numerator and the denominator by 2-sqrt(2), and we end up with:
16*sqrt(2)/2=x or x=8*sqrt(2)

This is one of the options, because the GMAT is trying to trick you into picking it. However, we are looking for the hypotenuse and this is one of the sides, so we have to multiply it by sqrt(2) and we get 16 (B)
_________________

Eliza
GMAT Tutor
bestgmatprepcourse.com

Kudos [?]: 27 [0], given: 0

Director
Director
User avatar
Joined: 10 Mar 2013
Posts: 589

Kudos [?]: 492 [0], given: 200

Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
GMAT ToolKit User
Re: The perimeter of a certain isosceles right triangle is 16 + [#permalink]

Show Tags

New post 14 Jan 2016, 01:47
coffeeloverfreak wrote:
The perimeter of a certain isosceles right triangle is \(16 + 16 \sqrt{2}\). What is the length of the hypotenuse of the triangle?

\((A) \hspace{5} 8\)
\((B) \hspace{5} 16\)
\((C) \hspace{5} 4\sqrt{2}\)
\((D) \hspace{5} 8\sqrt{2}\)
\((E) \hspace{5} 16\sqrt{2}\)


isosceles right triangle = x, x, x \sqrt{2}
So we can have here only two cases, in which 2 sides are equal:
1. Sides = 8, 8 and \(Hypotenuse=16 \sqrt{2}\) --> \(Hypotenuse^2=8^2+8^2 is not equal to 16 \sqrt{2}\), NO
2. \(Sides = 8 \sqrt{2}, 8 \sqrt{2}\), \(Hypotenuse=16\)--> \(Hypotenuse^2=(8 \sqrt{2})^2+(8 \sqrt{2})^2=16\) YES
Answer B
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Kudos [?]: 492 [0], given: 200

Expert Post
2 KUDOS received
SVP
SVP
User avatar
G
Joined: 11 Sep 2015
Posts: 1904

Kudos [?]: 2741 [2], given: 364

Location: Canada
Re: The perimeter of a certain isosceles right triangle is 16 + [#permalink]

Show Tags

New post 19 Apr 2016, 17:14
2
This post received
KUDOS
Expert's post
Quote:
The Perimeter of a certain isosceles right triangle is 16 + 16√2. What is the length of the hypotenuse of the triangle?

A) 8
B) 16
C) 4√2
D) 8√2
E) 16√2


An IMPORTANT point to remember is that, in any isosceles right triangle, the sides have length x, x, and x√2 for some positive value of x.

Note: x√2 is the length of the hypotenuse, so our goal is to find the value of x√2

From here, we can see that the perimeter will be x + x + x√2

In the question, the perimeter is 16 + 16√2, so we can create the following equation:
x + x + x√2 = 16 + 16√2,
Simplify: 2x + x√2 = 16 + 16√2
IMPORTANT: Factor x√2 from the left side to get : x√2(√2 + 1) = 16 + 16√2
Now factor 16 from the right side to get: x√2(√2 + 1) = 16(1 + √2)
Divide both sides by (1 + √2) to get: x√2 = 16

Answer = B

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2741 [2], given: 364

Expert Post
1 KUDOS received
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5345

Kudos [?]: 6111 [1], given: 121

Re: The perimeter of a certain isosceles right triangle is 16 + [#permalink]

Show Tags

New post 19 Apr 2016, 20:00
1
This post received
KUDOS
Expert's post
Flexxice wrote:
The perimeter of a certain isosceles triangle is 16 + 16 * square root of 2. What is the length of the hypotenuse of the triangle?

A) 8

B) 16

C) 4 * square root of 2

D) 8 * square root of 2

E) 16 * square root of 2



Firstly you have missed out onright angle in "certain isosceles triangle"..
secondly..
16 +16\(\sqrt{2}\) should tell us that the two equal sides are either 8 or 8\(\sqrt{2}\)..
If it is 8, perimeter = 8+8+8\(\sqrt{2}\), which is not the case here..
if it is 8\(\sqrt{2}\), P = 8\(\sqrt{2}\)+8\(\sqrt{2}\)+8\(\sqrt{2}*\sqrt{2}\) = 16 + 16\(\sqrt{2}\).. which is the P
so side is 8\(\sqrt{2}\) and HYP = 16
B
OA is being edited accordingly
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6111 [1], given: 121

Manager
Manager
avatar
B
Joined: 08 Jan 2015
Posts: 86

Kudos [?]: 10 [0], given: 53

GMAT ToolKit User
Re: The perimeter of a certain isosceles right triangle is 16 + [#permalink]

Show Tags

New post 06 Aug 2016, 03:32
Very efficient solution is the following:
P=2a+b=16+16*sqrt(2), then it means that either 2a=16 and b=16*sqrt(2), or 2a=16*sqrt(2) and b=16. Since in triangle b<2a, then b=16 and a=8*sqrt(2). Then plug into a^2+a^2=b^2 and check if its works.

Kudos [?]: 10 [0], given: 53

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 23 Apr 2015
Posts: 332

Kudos [?]: 118 [1], given: 36

Location: United States
Concentration: General Management, International Business
WE: Engineering (Consulting)
Re: The perimeter of a certain isosceles right triangle is 16 + [#permalink]

Show Tags

New post 18 Aug 2016, 21:57
1
This post received
KUDOS
coffeeloverfreak wrote:
The perimeter of a certain isosceles right triangle is \(16 + 16 \sqrt{2}\). What is the length of the hypotenuse of the triangle?

\((A) \hspace{5} 8\)
\((B) \hspace{5} 16\)
\((C) \hspace{5} 4\sqrt{2}\)
\((D) \hspace{5} 8\sqrt{2}\)
\((E) \hspace{5} 16\sqrt{2}\)


Hence the answer is B) 16
Attachments

triangle1.PNG
triangle1.PNG [ 14.17 KiB | Viewed 785 times ]

Kudos [?]: 118 [1], given: 36

1 KUDOS received
Director
Director
User avatar
G
Joined: 26 Oct 2016
Posts: 690

Kudos [?]: 252 [1], given: 855

Location: United States
Concentration: Marketing, International Business
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Re: The perimeter of a certain isosceles right triangle is 16 + [#permalink]

Show Tags

New post 30 Dec 2016, 03:00
1
This post received
KUDOS
Let the hypotenuse be x, then the length of the leg is x/root2.
x+2x/root2=16+16*root2
x+root*x=16+16*root2
So, x=16
_________________

Thanks & Regards,
Anaira Mitch

Kudos [?]: 252 [1], given: 855

Intern
Intern
avatar
B
Joined: 20 Sep 2016
Posts: 26

Kudos [?]: [0], given: 115

Premium Member
Re: The perimeter of a certain isosceles right triangle is 16 + [#permalink]

Show Tags

New post 05 Nov 2017, 19:33
I am little confuse here. given that this is a Isosceles right angle triangle which can be either 30-60-90 triangle or 45-45-90.
I don't understand,why it should be intuitive to consider 45-45-90 triangle ?

would appreciate your response. thanks !

Kudos [?]: [0], given: 115

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42577

Kudos [?]: 135462 [0], given: 12695

Re: The perimeter of a certain isosceles right triangle is 16 + [#permalink]

Show Tags

New post 05 Nov 2017, 21:55
jyotipes21@gmail.com wrote:
I am little confuse here. given that this is a Isosceles right angle triangle which can be either 30-60-90 triangle or 45-45-90.
I don't understand,why it should be intuitive to consider 45-45-90 triangle ?

would appreciate your response. thanks !


An isosceles triangle is a triangle with at least two sides of the same length. An isosceles triangle also has at least two angles of the same measure; namely, the angles opposite to the two sides of the same length. So, 30-60-90 is NOT an isosceles triangle.

You should go through the basics once more.

Basics to Brush-Up Fundamentals




23. Geometry




24. Coordinate Geometry




25. Triangles




26. Polygons




27. Circles




28. Rectangular Solids and Cylinders




29. Graphs and Illustrations




For more check Ultimate GMAT Quantitative Megathread
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135462 [0], given: 12695

Re: The perimeter of a certain isosceles right triangle is 16 +   [#permalink] 05 Nov 2017, 21:55

Go to page   Previous    1   2   3   4   [ 75 posts ] 

Display posts from previous: Sort by

The perimeter of a certain isosceles right triangle is 16 +

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.