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

Redeem

Are all angles of triangle smaller than 90 degrees?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
Legendary Member
Posts: 1448
Joined: Tue May 17, 2011 9:55 am
Location: India
Thanked: 375 times
Followed by:53 members

by Frankenstein » Sat Aug 13, 2011 10:44 pm
Hi,
If a,b,c are the sides of triangle
If a^2<b^2+c^2, then angle A(opposite to side a) < 90 degrees
If a^2=b^2+c^2, then angle A(opposite to side a) = 90 degrees
If a^2>b^2+c^2, then angle A(opposite to side a) < 90 degrees
This is the concept.
From(1):
2AB = 3BC = 4AC = 12k(say)
So, AB = 6k, BC = 4k, AC = 3k
AB^2 = 36k^2
BC^2+AC^2 = 25k^2
So, AB^2 > BC^2+AC^2
Hence, angle C is greater than 90.
So, all angles of triangle are not less than 90.
Sufficient

From(2):
AC^2 + AB^2 > BC ^2
So, angle A is less than 90 degrees.
We are not sure about the other 2 angles
Not sufficient

Hence, A
Cheers!

Things are not what they appear to be... nor are they otherwise
Top
Post new topic Post Reply
• Page 1 of 1