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

It is currently 25 Oct 2014, 20:57

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

In the diagram above, <PQR is a right angle, and QS is

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 17 Oct 2010
Posts: 81
Followers: 1

Kudos [?]: 74 [0], given: 26

In the diagram above, <PQR is a right angle, and QS is [#permalink] New post 05 May 2012, 18:37
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

62% (02:08) correct 38% (01:35) wrong based on 58 sessions
Attachment:
Geometry.jpg
Geometry.jpg [ 3.7 KiB | Viewed 2427 times ]
In the diagram above, <PQR is a right angle, and QS is perpendicular to PR. If PS has a length of 25 and SR has a length of 4, what is the area of triangle PQR?

A. 125
B. 145
C. 240
D. 290
E. It cannot be determined
[Reveal] Spoiler: OA

Last edited by Bunuel on 06 May 2012, 01:25, edited 1 time in total.
Edited the question
1 KUDOS received
Intern
Intern
avatar
Joined: 06 May 2012
Posts: 2
Followers: 0

Kudos [?]: 1 [1] , given: 4

Re: Geometry [#permalink] New post 06 May 2012, 01:16
1
This post received
KUDOS
is it true?

25^2 + qs^2 = qp^2
4^2 + qs^2 = qr^2
and then (by sum them) you have:
625+16+2(qs^2)=qp^2+qr^2 *
and you know from the main triangle:
pq^2+qr^2=(pr)^2=(25+4)^2=841 **

from * and ** we have:

pq^2 +qr^2 = 841 = 625+16+2qs^2
2qs^2=841-641= 200
qs=10
then the area of PQR is:
10* (25+4)/2 = 145
Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23422
Followers: 3618

Kudos [?]: 28982 [2] , given: 2874

Re: In the diagram above, <PQR is a right angle, and QS is [#permalink] New post 06 May 2012, 01:43
2
This post received
KUDOS
Expert's post
BhaskarPaul wrote:
Attachment:
Geometry.jpg
Geometry.jpg [ 3.7 KiB | Viewed 2410 times ]
In the diagram above, <PQR is a right angle, and QS is perpendicular to PR. If PS has a length of 25 and SR has a length of 4, what is the area of triangle PQR?

A. 125
B. 145
C. 240
D. 290
E. It cannot be determined


Perpendicular to the hypotenuse always divides the triangle into two triangles with the same properties as the original triangle.

Thus, the perpendicular QS divides right triangle PRQ into two similar triangles PQS and QRS (which are also similar to the big triangle PRQ). Now, in these three triangles the ratio of the corresponding sides will be equal (corresponding sides are the sides opposite the same angles).

So, PS/QS=QS/SR --> QS^2=PS*SR=25*4=100 --> QS=10 --> area of PQR equals to 1/2*PR*QS=1/2*(PS+SR)*QS=1/2*29*10=145.

Answer: B.

For more on check 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: 17 Oct 2010
Posts: 81
Followers: 1

Kudos [?]: 74 [0], given: 26

Re: In the diagram above, <PQR is a right angle, and QS is [#permalink] New post 06 May 2012, 14:58
Bunuel wrote:
BhaskarPaul wrote:
Attachment:
Geometry.jpg
In the diagram above, <PQR is a right angle, and QS is perpendicular to PR. If PS has a length of 25 and SR has a length of 4, what is the area of triangle PQR?

A. 125
B. 145
C. 240
D. 290
E. It cannot be determined


Perpendicular to the hypotenuse always divides the triangle into two triangles with the same properties as the original triangle.

Thus, the perpendicular QS divides right triangle PRQ into two similar triangles PQS and QRS (which are also similar to the big triangle PRQ). Now, in these three triangles the ratio of the corresponding sides will be equal (corresponding sides are the sides opposite the same angles).

So, PS/QS=QS/SR --> QS^2=PS*SR=25*4=100 --> QS=10 --> area of PQR equals to 1/2*PR*QS=1/2*(PS+SR)*QS=1/2*29*10=145.

Answer: B.

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

Hope it helps.



ya that helps , great
Manager
Manager
avatar
Joined: 17 Oct 2010
Posts: 81
Followers: 1

Kudos [?]: 74 [0], given: 26

Re: Geometry [#permalink] New post 14 May 2012, 03:23
mehdi2012 wrote:
is it true?

25^2 + qs^2 = qp^2
4^2 + qs^2 = qr^2
and then (by sum them) you have:
625+16+2(qs^2)=qp^2+qr^2 *
and you know from the main triangle:
pq^2+qr^2=(pr)^2=(25+4)^2=841 **

from * and ** we have:

pq^2 +qr^2 = 841 = 625+16+2qs^2
2qs^2=841-641= 200
qs=10
then the area of PQR is:
10* (25+4)/2 = 145



This is also a good way to solve this problem if we find it difficult to apply similarity of triangles, though we have to find the squares of some numbers .
Intern
Intern
avatar
Joined: 19 Feb 2013
Posts: 4
Followers: 0

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

Re: Geometry [#permalink] New post 31 Jul 2013, 06:00
mehdi2012 wrote:
is it true?

25^2 + qs^2 = qp^2
4^2 + qs^2 = qr^2
and then (by sum them) you have:
625+16+2(qs^2)=qp^2+qr^2 *
and you know from the main triangle:
pq^2+qr^2=(pr)^2=(25+4)^2=841 **

from * and ** we have:

pq^2 +qr^2 = 841 = 625+16+2qs^2
2qs^2=841-641= 200
qs=10
then the area of PQR is:
10* (25+4)/2 = 145






How do we figure out which side is proportional to which using angles? :S
Intern
Intern
avatar
Joined: 02 Feb 2012
Posts: 29
GPA: 4
Followers: 0

Kudos [?]: 7 [0], given: 35

Re: In the diagram above, <PQR is a right angle, and QS is [#permalink] New post 01 Aug 2013, 19:37
Bunuel wrote:
BhaskarPaul wrote:
Attachment:
Geometry.jpg
In the diagram above, <PQR is a right angle, and QS is perpendicular to PR. If PS has a length of 25 and SR has a length of 4, what is the area of triangle PQR?

A. 125
B. 145
C. 240
D. 290
E. It cannot be determined


Perpendicular to the hypotenuse always divides the triangle into two triangles with the same properties as the original triangle.

Thus, the perpendicular QS divides right triangle PRQ into two similar triangles PQS and QRS (which are also similar to the big triangle PRQ). Now, in these three triangles the ratio of the corresponding sides will be equal (corresponding sides are the sides opposite the same angles).

So, PS/QS=QS/SR --> QS^2=PS*SR=25*4=100 --> QS=10 --> area of PQR equals to 1/2*PR*QS=1/2*(PS+SR)*QS=1/2*29*10=145.

Answer: B.

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

Hope it helps.


Corresponding angles are QPS and QRS right.
In that case, it must be PS/QS=SR/QS..

Please let me know where I am wrong...
Re: In the diagram above, <PQR is a right angle, and QS is   [#permalink] 01 Aug 2013, 19:37
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic In the diagram to the right, triangle ABC has a right angle abhijit_sen 17 03 Jul 2008, 15:12
Experts publish their posts in the topic In the diagram to the right, triangle PQR has a right angle applecrisp 7 01 Dec 2007, 22:44
8 Experts publish their posts in the topic In the diagram to the right, triangle PQR has a right angle jimjohn 6 31 Oct 2007, 08:07
In the diagram to the right, triangle PQR has a right angle Piter 13 23 Aug 2007, 12:55
1 In the diagram to the right, triangle PQR has a right angle Witchiegrlie 17 13 Apr 2007, 09:12
Display posts from previous: Sort by

In the diagram above, <PQR is a right angle, and QS is

  Question banks Downloads My Bookmarks Reviews Important topics  


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®.