# CAT Practice : Coordinate Geometry

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Find out the value of x.

Q.36: If PQ∥RS, find the value of x

1. 7
2. 3
3. Both A & B
4. None of these

Choice (C). Both A & B

## Detailed Solution

If PQ∥RS =) ∆POQ ~ ∆ROS
=) ${\frac{1}{(x+5)} = \frac{(x - 2)}{(13x - 31)}}$
=) 13x - 31 = (x-2)(x+5)
=) 13x – 31 = x2 – 2x + 5x – 10
=) 13x – 31 = x2 + 3x – 10
=) x2 – 10x +21 = 0
=) x2 – 7x – 3x +21 = 0
=) x(x-7) -3(x-7) = 0
=) (x-3)(x-7) = 0
=) x = 3, 7
=) (C) Ans

Correct Answer: (C). = Both A & B

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