Geometric Questions Answers

Geometry - Quant/Math - CAT 2008

Question 4 the day: October 09, 2003

The question for the day is from the topic of Geometry.

If ABC is a right angle triangle with angle A = 900 and 2s = a + b + c, where a > b > c where notations have their usual meanings, then which one of the following is correct?

(1)	(s � b) (s � c) > s (s � a)			(2)	(s � a) (s � c) > s (s � b)
(3)	(s � a) (s � b) < s (s � c)			(4)	4s (s � a) (s � b) (s � c) = bc

Correct Answer - (3)

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Solution:


Let a = 5, b = 4 & c = 3

Since it is a right angle triangle and 3, 4 and 5 are pythogorean triplet.

s = (a + b + c)/2 = 12/2 = 6

Substitute these values and check which condition satisfies this.

Let us take choice(3)

L.H.S

(s � a) (s � b) = (6 - 5)(6 - 4) = 2.

R.H.S

s(s � c) = 6(6 � 3) = 18.

L.H.S < R.H.S

It satisfies the given condition hence Choice(3) is the right answer.