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

Redeem

Right Triangle Problem

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Newbie | Next Rank: 10 Posts
Posts: 9
Joined: Fri Sep 24, 2010 12:26 pm

Right Triangle Problem

by omair_bba » Sun Aug 26, 2012 7:08 am
Hi, I am just starting the prep. of GMAT. Below Q is not from any OG.

Q: Two sides of right triangle are 12 & 13. Which of the following could be the length of the third side.
I. 5 II. 11 III. Sqrt 313

A) I only
B) II only
C) I & II only
D) I & III only
E) I,II & III


My Understanding:
* 5 can be the side (Since a Pythagorean triple I remembered)
* Also by geometry rule (The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.) For two given sides 12,13 the third side (e.g X) should be 1 < X > 25.

Therefore should'nt answer be E

Thanx...
Top
Source: — Quantitative Reasoning |
User avatar
MBA Admissions Consultant
Posts: 2279
Joined: Fri Nov 11, 2011 7:51 am
Location: New York
Thanked: 660 times
Followed by:266 members
GMAT Score:770

by Jim@StratusPrep » Sun Aug 26, 2012 7:47 am
You won't be able to form a right triangle with 11 as the side. The two legs must be the smallest two sides. If 11 and 12 are the legs then the length of the hypotenuse would be sqrt(265) and not 13.
GMAT Answers provides a world class adaptive learning platform.
-- Push button course navigation to simplify planning
-- Daily assignments to fit your exam timeline
-- Organized review that is tailored based on your abiility
-- 1,000s of unique GMAT questions
-- 100s of handwritten 'digital flip books' for OG questions
-- 100% Free Trial and less than $20 per month after.
-- Free GMAT Quantitative Review

Image
Top
User avatar
Newbie | Next Rank: 10 Posts
Posts: 9
Joined: Fri Sep 24, 2010 12:26 pm

by omair_bba » Sun Aug 26, 2012 8:31 am
@ Jim@StratusPrep Thanks for the reply !

Please tell where I am wrong with the concept..
(The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.) For two given sides 12,13 the third side (e.g X) should be 1 < X > 25.
And is the correct answer D then ?
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Mon Aug 27, 2012 7:49 am
omair_bba wrote: Please tell where I am wrong with the concept..
(The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.) For two given sides 12,13 the third side (e.g X) should be 1 < X > 25.
This rule applies to all triangles (right triangles and non-right triangles).
If we removed the "right triangle" restriction from the original question, then we could apply your rule. However, as it stands, the "right triangle" restriction limits our solution even further.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Mon Aug 27, 2012 7:57 am
omair_bba wrote: Q: Two sides of right triangle are 12 & 13. Which of the following could be the length of the third side.
I. 5 II. 11 III. Sqrt 313

A) I only
B) II only
C) I & II only
D) I & III only
E) I,II & III
Since we're talking about a right triangle, we can apply the Pythagorean Theorem (a^2 + b^2 = c^2)

We must consider two cases:

case 1: the length of the hypotenuse (the longest side) is 13.
In this case, the missing side is a leg.
If we let x = the length of the missing side, we can write x^2 + 12^2 = 13^2
Solve to get x=5

case 2: the length of the hypotenuse (the longest side) is not 13.
Notice that 12 cannot be the length of the hypotenuse, since it would not be the longest side.
So, the missing side must be the hypotenuse.
If we let x = the length of the missing side, we can write 12^2 + 13^2 = x^2
Solve:
144 + 169 = x^2
313 = x^2
x = sqrt(313)

So, the missing side can have length 5 or sqrt(313)

The answer is D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1