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

It is currently 21 Oct 2014, 16:09

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:
Intern
Intern
User avatar
Joined: 10 Feb 2007
Posts: 46
Followers: 0

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

In the diagram to the right, triangle PQR has a right angle [#permalink] New post 13 Apr 2007, 09:12
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?

see attached JPEG

3/2

7/4

15/8

16/9

2

[/img]
Attachments

triangle.jpg
triangle.jpg [ 6.39 KiB | Viewed 1242 times ]

Director
Director
User avatar
Joined: 26 Feb 2006
Posts: 908
Followers: 4

Kudos [?]: 44 [0], given: 0

Re: 700 level Geo Question [#permalink] New post 13 Apr 2007, 11:53
Witchiegrlie 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?

see attached JPEG

3/2

7/4

15/8

16/9

2


I donot know the best way;

b = 15
l = 20
h = 25.

solving for the areas of the triangles, the ratio = 16/9.
Director
Director
User avatar
Joined: 14 Jan 2007
Posts: 782
Followers: 2

Kudos [?]: 56 [0], given: 0

 [#permalink] New post 13 Apr 2007, 13:21
My answer is 'D'.
I have used the long way to solve this. Somebody please suggest some quick approach.
Director
Director
avatar
Joined: 18 Jul 2006
Posts: 532
Followers: 1

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

 [#permalink] New post 13 Apr 2007, 15:40
Got D.
After solving, we get PQ=20, PR=25 and QR=15, PS=16, RS=9
(Area PQS)/(Area PRS) = PS/RS = 16/9
Intern
Intern
avatar
Joined: 10 Mar 2007
Posts: 4
Followers: 0

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

 [#permalink] New post 13 Apr 2007, 19:18
Anybody please explain your solution to this problem.
1 KUDOS received
Current Student
avatar
Joined: 28 Dec 2004
Posts: 3403
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 164 [1] , given: 2

 [#permalink] New post 14 Apr 2007, 09:37
1
This post received
KUDOS
OK..you need to memorize the famous triangles..right angle triangles, usually come in the size 3:4:5, 6:8:10 5:12:13..check it for yourself..

so we know the perimeter: is 60

3X+4x+5x=60; x= 5...

OK..so we know that PQ=20, PR=25 and QR=15.

Ok...lets see the second triangle PQS is again 3:4:5, cause we know that QR=15, the other line is 12, so we know the other line is 9.

alright..now area of triangle = 0.5 base*height.. well get rid of the 0.5 cause they will cancel out in the ratio.

so we have...PQS=base=12 heigth=16; i.e 25-9. so 12*16
QRS base=9 height=12...

now PQS/QRS=16/9

Hope this helps...


jaspetrovic wrote:
Anybody please explain your solution to this problem.
VP
VP
User avatar
Joined: 03 Apr 2007
Posts: 1377
Followers: 3

Kudos [?]: 194 [0], given: 10

Reviews Badge
[#permalink] New post 14 Apr 2007, 13:32
fresinha12 wrote:
OK..you need to memorize the famous triangles..right angle triangles, usually come in the size 3:4:5, 6:8:10 5:12:13..check it for yourself..

so we know the perimeter: is 60

3X+4x+5x=60; x= 5...

OK..so we know that PQ=20, PR=25 and QR=15.

Ok...lets see the second triangle PQS is again 3:4:5, cause we know that QR=15, the other line is 12, so we know the other line is 9.

alright..now area of triangle = 0.5 base*height.. well get rid of the 0.5 cause they will cancel out in the ratio.

so we have...PQS=base=12 heigth=16; i.e 25-9. so 12*16
QRS base=9 height=12...

now PQS/QRS=16/9

Hope this helps...


jaspetrovic wrote:
Anybody please explain your solution to this problem.


Very well explained
Intern
Intern
User avatar
Joined: 10 Feb 2007
Posts: 46
Followers: 0

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

 [#permalink] New post 14 Apr 2007, 17:51
Thanks fresinha12! The easiest way so far......
Manager
Manager
avatar
Joined: 12 Feb 2007
Posts: 167
Followers: 1

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

 [#permalink] New post 15 Apr 2007, 10:35
How do we know they are 3-4-5 triangles?
Director
Director
avatar
Joined: 24 Aug 2006
Posts: 754
Location: Dallas, Texas
Followers: 5

Kudos [?]: 30 [0], given: 0

 [#permalink] New post 15 Apr 2007, 22:06
Tuneman wrote:
How do we know they are 3-4-5 triangles?


Assuming it to be 3-4-5 triangle can be a fatal mistake.

You need to solve three equations:

xy=12z
x^2+y^2=z^2
x+y+z=60

This will give you individual length of the arms.

15-20-25 (luckily it was 3-4-5 triangle)
_________________

"Education is what remains when one has forgotten everything he learned in school."

Manager
Manager
avatar
Joined: 28 Aug 2006
Posts: 160
Followers: 2

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

 [#permalink] New post 16 Apr 2007, 13:29
Where did you get XY=12Z ? Is there an theorm or eqn outthere. Please shed some light.
Manager
Manager
avatar
Joined: 12 Feb 2007
Posts: 167
Followers: 1

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

 [#permalink] New post 16 Apr 2007, 13:43
Swagatalakshmi wrote:
Tuneman wrote:
How do we know they are 3-4-5 triangles?


Assuming it to be 3-4-5 triangle can be a fatal mistake.

You need to solve three equations:

xy=12z
x^2+y^2=z^2
x+y+z=60

This will give you individual length of the arms.

15-20-25 (luckily it was 3-4-5 triangle)


yes I was looking for 3 eqns also, but like the above poster mentioned, where did you get that xy=12z?


This seems to be a 4-5 minute problem
Intern
Intern
avatar
Joined: 11 Apr 2007
Posts: 1
Followers: 0

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

 [#permalink] New post 17 Apr 2007, 00:49
the area of the triangle is 1/2*x*y
the area of the two small triangles are 1/2*z*12

therefore, 1/2*x*y=1/2*z*12

x*y=12*z


got it?...
Director
Director
User avatar
Joined: 09 Aug 2006
Posts: 529
Followers: 2

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

 [#permalink] New post 17 Apr 2007, 11:34
chris743 wrote:
the area of the triangle is 1/2*x*y
the area of the two small triangles are 1/2*z*12

therefore, 1/2*x*y=1/2*z*12

x*y=12*z


got it?...


There is a flaw in u r argument.. The two smaller triangles are not same.. so both of them can't be 1/2*z*12
Manager
Manager
avatar
Joined: 17 Apr 2007
Posts: 93
Followers: 1

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

 [#permalink] New post 17 Apr 2007, 13:18
Amit05 wrote:
chris743 wrote:
the area of the triangle is 1/2*x*y
the area of the two small triangles are 1/2*z*12

therefore, 1/2*x*y=1/2*z*12

x*y=12*z


got it?...


There is a flaw in u r argument.. The two smaller triangles are not same.. so both of them can't be 1/2*z*12


area of triangle PQR can also be found using 1/2*PR*QS (QS is perpendicular to PR)- 1/2*z*12
Manager
Manager
avatar
Joined: 11 Nov 2006
Posts: 144
Followers: 1

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

 [#permalink] New post 29 Apr 2007, 00:47
[quote="fresinha12"]OK..you need to memorize the famous triangles..right angle triangles, usually come in the size 3:4:5, 6:8:10 5:12:13..check it for yourself..

so we know the perimeter: is 60

3X+4x+5x=60; x= 5...

OK..so we know that PQ=20, PR=25 and QR=15.

Ok...lets see the second triangle PQS is again 3:4:5, cause we know that QR=15, the other line is 12, so we know the other line is 9.

alright..now area of triangle = 0.5 base*height.. well get rid of the 0.5 cause they will cancel out in the ratio.

so we have...PQS=base=12 heigth=16; i.e 25-9. so 12*16
QRS base=9 height=12...

now PQS/QRS=16/9

Hope this helps...

Hi Fresinha, could you please explain what was your criteria to select the right triangle 3:4:5? (..3x+4x+5x=60) ?
Manager
Manager
User avatar
Joined: 30 Mar 2007
Posts: 222
Followers: 1

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

 [#permalink] New post 29 Apr 2007, 08:09
The greatest common divisor of the three numbers 3, 4, and 5 is 1.

Pythagorean triples with this property are called primitive.

From primitive Pythagorean triples, you can get other, imprimitive ones, by multiplying each of a, b, and c by any positive whole number d > 1. This is because
a^2 + b^2 = c^2

if and only if (da)^2 + (db)^2 = (dc)^2.

Thus (a,b,c) is a Pythagorean triple if and only if (da,db,dc) is. For example, (6,8,10) and (9,12,15) are imprimitive Pythagorean triples.


Guess we should know few of the primitive triplets

And then hit and trail

Few of starting the primitive triplets


3 4 5
5 12 13
15 8 17
7 24 25
21 20 29
9 40 41
35 12 37
11 60 61
45 28 53

Please let me know if this makes sense
Manager
Manager
avatar
Joined: 11 Mar 2007
Posts: 69
Followers: 1

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

 [#permalink] New post 29 Apr 2007, 09:12
I found these thereoms...

- If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other

- In a right triangle, the length of the altitude from the right angle to the hypotenuse is the geometric mean of the lengths of the two segments of the hypotenuse

- In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. Each leg of the right triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg

- The areas of two similar triangles are proportional to the squares of any two homologous sides.

However, I still can't solve the question. I just run around in circles. Maybe these can help jar something loose in someone else...
  [#permalink] 29 Apr 2007, 09:12
    Similar topics Author Replies Last post
Similar
Topics:
7 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
38 Experts publish their posts in the topic In the diagram, triangle PQR has a right angle at Q and a enigma123 24 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
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
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®.