triangle..

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srivathsan: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Sat Aug 25, 2012 9:43 pm

triangle..

by srivathsan » Mon Aug 27, 2012 9:27 am

A triangle has side of lengths 1, 1 and S. what are the possible values of S for which the triangle is obtuse?

a. 1<_ S <_ 2
b. 1<S<2
c. Sq.root of 2 <_ S <_ 2
d. Sq.root of 2 <_ S < 2
e. Sq.root of 2 < S < 2

Kindly help me..Im sure option a,b & e is not the answer. Help me

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Source: Beat The GMAT — Problem Solving | Mon Aug 27, 2012 9:27 am

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 am; Location: Utrecht, The Netherlands; Thanked: 318 times; Followed by:52 members

by neelgandham » Mon Aug 27, 2012 7:31 pm

a. 1<S<2 - Let the value of S be 1, then the triangle formed is an equilateral triangle. So, answer choice 1 is not the answer.
b. 1<S<2 - Let the value of S be âˆš2, then the triangle formed is a right angled triangle. So, answer choice 2 is not the answer
c. âˆš2 [/u] S [/u] 2 - Let the value of S be âˆš2, then the triangle formed is a right angled triangle. So, answer choice 2 is not the answer
d. âˆš2 [/u] S < 2 - Let the value of S be âˆš2, then the triangle formed is a right angled triangle. So, answer choice 2 is not the answer
e. âˆš2 < S < 2 - The leftover and the answer

Just curious, How did you eliminate a,b & e?

Anil Gandham
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everything's eventual: Master | Next Rank: 500 Posts; Posts: 101; Joined: Sun Jun 03, 2012 10:10 pm; Thanked: 10 times; Followed by:1 members

by everything's eventual » Mon Aug 27, 2012 8:29 pm

For the triangle to be obtuse one of the angles has a measure of greater than 90 degrees.

If the triangle is a right triangle then the value of S will be sqrt 2 ( pythagoras theorem)

Thus S has to be greater than sqrt 2.

a. 1<_ S <_ 2 - S can be less than sqrt 2 in this option. So this is not the answer.
b. 1<S<2 - S can be still be less than sqrt 2 in this option ( eg : S = 1.1). So this is no the answer.
c. Sq.root of 2 <_ S <_ 2 - Here S can be equal to sqrt 2 which would make it a right triangle. So not the answer.
d. Sq.root of 2 <_ S < 2 - Same as above.
e. Sq.root of 2 < S < 2 - This is the right answer as S has to be greater than sqrt 2.