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

It is currently 23 Jul 2014, 08:37

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 to the right, triangle PQR has a right angle

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 19 Aug 2007
Posts: 170
Followers: 1

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

In the diagram to the right, triangle PQR has a right angle [#permalink] New post 31 Oct 2007, 08:07
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (medium)

Question Stats:

57% (05:23) correct 43% (03:17) wrong based on 74 sessions
In the diagram to the right, triangle PQR has a right angle at Q and a perimeter of 60. Line segment QS is perpendicular to PR and has a length of 12. PQ > QR. What is the ratio of the area of triangle PQS to the area of triangle RQS?

A.. 3/2
B. 7/4
C. 15/8
D. 16/9
E. 2
Attachment:
triangle.jpg
triangle.jpg [ 6.39 KiB | Viewed 2822 times ]


OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-diagram-triangle-pqr-has-a-right-angle-at-q-and-a-127093.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 15 Apr 2012, 23:46, edited 1 time in total.
Edited the question and added the OA. Topic is locked.
Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesGMAT Pill GMAT Discount Codes
2 KUDOS received
Director
Director
avatar
Joined: 11 Jun 2007
Posts: 932
Followers: 1

Kudos [?]: 42 [2] , given: 0

GMAT Tests User
Re: PS Triangle [#permalink] New post 31 Oct 2007, 08:47
2
This post received
KUDOS
jimjohn wrote:
In the diagram to the right, triangle PQR has a right angle at Q and a perimeter of 60. Line segment QS is perpendicular to PR and has a length of 12. PQ > QR. What is the ratio of the area of triangle PQS to the area of triangle RQS?


3/2

7/4

15/8

16/9

2


i get 16/9 but after spending too much time trying to figure it out. :(
i'll try my best to explain as best as i can (see my diagram below)

stem only tells you 1) these three triangles are all right triangles (so you can easily apply pythagorean theorem), 2) the perimeter of the largest triangle, 3) the length of the bisector, and 4) PQ > QR. From this you have to think about the possible lengths to find the sides.

I thought about the common right triangle sides: 3-4-5, 6-8-10, etc and saw that 3-4-5 = 12 and 60 is a multiple of 12 (5x). So the possible sides are [3-4-5]*5 = 15-20-25. But first have to test it out. We know that PQ > QR and the largest side is the hypotenuse. So PQ = 20, QR = 15, and PR = 25. From there I used side QS = 12 to figure out the splits between PS and RS. (Lucky thing it worked out!!)

PS^2 + QS^2 = PQ^2
PS^2 = PQ^2 - QS^2
400 - 144 = 256
sqrt256 = 16

QS^2 + RS^2 = QR^2
RS^2 = QR^2 - QS^2
225 - 144 = 81
sqrt 81 = 9

so the ratio of the area of triangle PQS to the area of triangle RQS is
PQS = 1/2bh
1/2 * 12 * 16 = 96

RQS = 1/2bh
1/2 * 12 * 9 = 54

96:54 = 16:9

Attachments

geometry.JPG
geometry.JPG [ 9.88 KiB | Viewed 2793 times ]


Last edited by beckee529 on 31 Oct 2007, 08:54, edited 2 times in total.
Current Student
User avatar
Joined: 18 Jun 2007
Posts: 408
Location: Atlanta, GA
Schools: Emory class of 2010
Followers: 10

Kudos [?]: 33 [0], given: 0

GMAT Tests User
 [#permalink] New post 31 Oct 2007, 08:53
Yeah, and actually, your calculations were still correct. I made an error in my calculations, the answer is not 2. It is 16/9 as you stated.
Director
Director
avatar
Joined: 11 Jun 2007
Posts: 932
Followers: 1

Kudos [?]: 42 [0], given: 0

GMAT Tests User
 [#permalink] New post 31 Oct 2007, 08:55
emoryhopeful wrote:
Yeah, and actually, your calculations were still correct. I made an error in my calculations, the answer is not 2. It is 16/9 as you stated.


yeah i had it right on paper but wrote it incorrectly on the computer screen :) but have since edited to correct it ;)
Senior Manager
Senior Manager
User avatar
Joined: 28 Jun 2009
Posts: 456
Location: United States (MA)
Followers: 14

Kudos [?]: 99 [0], given: 46

GMAT Tests User
Re: In the diagram to the right, triangle PQR has a right angle [#permalink] New post 15 Apr 2012, 17:27
How about this?

we've given that the hypotenuse of triangle PQR is 25.
Applying Pythagorean triplet 15-20-25,

PQ and QR are respectively 20 and 15.

So area = 1/2 * base QR * height PQ
= 1/2 * 15 * 20
= 150
Manager
Manager
avatar
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 235
Schools: Johnson '15
Followers: 2

Kudos [?]: 20 [0], given: 16

GMAT Tests User
Re: In the diagram to the right, triangle PQR has a right angle [#permalink] New post 15 Apr 2012, 20:52
jimjohn wrote:
In the diagram to the right, triangle PQR has a right angle at Q and a perimeter of 60. Line segment QS is perpendicular to PR and has a length of 12. PQ > QR. What is the ratio of the area of triangle PQS to the area of triangle RQS?


3/2

7/4

15/8

16/9

2


can somebody give OA for this?

_________________

Regards,
Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat ;)

Satyameva Jayate - Truth alone triumphs

Expert Post
4 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18696
Followers: 3236

Kudos [?]: 22266 [4] , given: 2602

Re: In the diagram to the right, triangle PQR has a right angle [#permalink] New post 15 Apr 2012, 23:45
4
This post received
KUDOS
Expert's post
harshavmrg wrote:
can somebody give OA for this?


In the diagram, triangle PQR has a right angle at Q and a perimeter of 60. Line segment QS is perpendicular to PR and has a length of 12. PQ > QR. What is the ratio of the area of triangle PQS to the area of triangle RQS?
A. 3/2
B. 7/4
C. 15/8
D. 16/9
E. 2
Attachment:
Triangle PQR.GIF
Triangle PQR.GIF [ 2.52 KiB | Viewed 2553 times ]


Let PQ=x, QR=y and PR=z.

Given: x+y+z=60 (i);
Equate the areas: \frac{1}{2}*xy=\frac{1}{2}*QS*z (area of PQR can be calculated by 1/2*leg*leg and 1/2* perpendicular to hypotenuse*hypotenuse) --> xy=12z (ii);
Aslo x^2+y^2=z^2 (iii);

So, we have:
(i) x+y+z=60;
(ii) xy=12z;
(iii) x^2+y^2=z^2.

From (iii) (x+y)^2-2xy=z^2 --> as from (i) x+y=60-z and from (ii) xy=12z then (60-z)^2-2*12z=z^2 --> 3600-120z+z^2-24z=z^2 --> 3600=144z --> z=25;

From (i) x+y=35 and from (ii) xy=300 --> solving for x and y --> x=20 and y=15 (as given that x>y).

Next, perpendicular to the hypotenuse will always divide the triangle into two triangles with the same properties as the original triangle. So, PQR and SQR are similar. In two similar triangles, the ratio of their areas is the square of the ratio of their sides: \frac{AREA}{area}=\frac{S^2}{s^2}.

So, \frac{x^2}{y^2}=\frac{AREA}{area} --> \frac{AREA}{area}=\frac{400}{225}=\frac{16}{9}

Answer: D.

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-diagram-triangle-pqr-has-a-right-angle-at-q-and-a-127093.html

_________________

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

Re: In the diagram to the right, triangle PQR has a right angle   [#permalink] 15 Apr 2012, 23:45
    Similar topics Author Replies Last post
Similar
Topics:
5 Experts publish their posts in the topic In the diagram to the right, triangle PQR has a right angle sudeeptasahu29 11 28 Mar 2014, 23:17
32 Experts publish their posts in the topic In the diagram, triangle PQR has a right angle at Q and a enigma123 22 05 Feb 2012, 15:54
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
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 to the right, triangle PQR has a right angle

  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®.