BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Area of a right-angled triangle

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 168
Joined: Thu Nov 01, 2012 7:43 pm
Thanked: 1 times

Area of a right-angled triangle

by pareekbharat86 » Sat Nov 09, 2013 11:30 pm
In a triangle PQR, angle PQR is a right angle. QS is a line segment drawn on the hypotenuse and perpendicular to the hypotenuse. Line segment PS is 25, line segment RS is 4. What is the area of the triangle PQR?

a. 125
b.145
c. 240
d. 290
e. Cannot be determined

OA is B.

The explanation says that triangles PQS and PRS are similar to triangle PQR. How?

Source- Kaplan Practice Test 3
Last edited by pareekbharat86 on Mon Nov 11, 2013 8:33 am, edited 2 times in total.
Thanks,
Bharat.
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pm
Thanked: 448 times
Followed by:34 members
GMAT Score:650

by theCodeToGMAT » Sun Nov 10, 2013 12:55 am
pareekbharat86 wrote:In a triangle PQR, angle PQR is a right angle. PS is a line segment drawn on the hypotenuse and perpendicular to the hypotenuse. Line segment QS is 24, line segment RS is 4. What is the area of the triangle PQR?

a. 125
b.145
c. 240
d. 290
e. Cannot be determined

OA is B.

The explanation says that triangles PQS and PRS are similar to triangle PQR. How?

Source- Kaplan Practice Test 3
Is there a typo in the question?
R A H U L
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Sun Nov 10, 2013 12:58 am
Hi Bharat,

Have you transcribed this question correctly?

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Master | Next Rank: 500 Posts
Posts: 168
Joined: Thu Nov 01, 2012 7:43 pm
Thanked: 1 times

by pareekbharat86 » Sun Nov 10, 2013 2:19 am
theCodeToGMAT wrote:
pareekbharat86 wrote:In a triangle PQR, angle PQR is a right angle. PS is a line segment drawn on the hypotenuse and perpendicular to the hypotenuse. Line segment QS is 24, line segment RS is 4. What is the area of the triangle PQR?

a. 125
b.145
c. 240
d. 290
e. Cannot be determined

OA is B.

The explanation says that triangles PQS and PRS are similar to triangle PQR. How?

Source- Kaplan Practice Test 3
Is there a typo in the question?
The error is regretted. I have edited the question.
Thanks,
Bharat.
Top
User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pm
Thanked: 448 times
Followed by:34 members
GMAT Score:650

by theCodeToGMAT » Sun Nov 10, 2013 2:43 am
I tried ... but got bit different answer.. are you sure of the value of measurements?
Attachments
solution.JPG
R A H U L
Top
User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pm
Thanked: 448 times
Followed by:34 members
GMAT Score:650

by theCodeToGMAT » Sun Nov 10, 2013 2:47 am
A Direct Shortcut
Attachments
solution.JPG
R A H U L
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sun Nov 10, 2013 4:26 am
I believe that the problem should read as follows:
In a triangle PQR, angle PQR is a right angle. QS is a line segment drawn on the hypotenuse and perpendicular to the hypotenuse. Line segment PS is 25, line segment RS is 4. What is the area of the triangle PQR?

a. 125
b.145
c. 240
d. 290
e. Cannot be determined
Image

QS is a height drawn through the right angle of triangle PQR.

A height drawn through the right angle of a triangle forms THREE SIMILAR TRIANGLES.

In the figure above:
The angles of triangle PQS are x-y-90.
The angles of triangle QRS are x-y-90.
The angles of triangle PQR are x-y-90.
Since each triangle has the same combination of angles, the 3 triangles are similar.

Since triangle PQS is similar to triangle QRS, the ratio of the legs in each triangle must be the same.
In triangle PQS:
(side opposite x)/(side opposite y) = h/25.
In triangle QRS:
(side opposite x)/(side opposite y) = 4/h.
Since the ratios must be equal:
h/25= 4/h
h² = 4*25
h = 2*5 = 10.

Area of PQR = (1/2)bh = (1/2)(29)(10) = 145.

The correct answer is B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1