triangle..

[srivathsan]

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

[neelgandham]

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

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

[everything's eventual]

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.

[mehaksal]

E is right coz side has to be >sqrt(2)