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Geometry - Quant/Math - CAT 2009
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) |
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(2) |
(s – a) (s – c) > s (s – b) |
| (3) |
(s – a) (s – b) < s (s – c) |
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(4) |
4s (s – a) (s – b) (s – c) = bc |
Correct Answer - (3)
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.
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