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CAT 2008 — QA Question 16

Basics of QuadrilateralsEasy
Passage / Data

Directions for next 2 questions:

The figure below shows the plan of a town. The streets are at right angles to each other. A rectangular park (P) is situated inside the town with a diagonal road running through it. There is also a prohibited region (D) in the town.

Consider a square ABCD with midpoints E, F, G, H of AB, BC, CD and DA respectively. Let L denote the line passing through F and H. Consider points P and Q, on L and inside ABCD, such that the angles APD and BQC both equal 120°. What is the ratio of the area of ABQCDP to the remaining area inside ABCD?

Answer & solution

  • A

    423

  • B

    2+3

  • C

    10-339

  • D

    1+13

  • 23-1

Solution

Let the length of the sides of the square be 2s.

Consider ∆BQF,

BF = s

In 30° - 60° - 90° triangle,

QF = s3

∴ Area of ∆BQF = 12 × s × s3

Area of ABQCDP = Area of square ABCD – 4 × Area of ∆BQF =4s2-4(12×s×s3)

∴ Required ratio = 4s2-4(12×s×s3)4(12×s×s3) = 23-1

Hence, option (e).

CAT 2008 QA Q16: Consider a square ABCD with midpoints E, F, G, H of AB, BC, CD and DA respectively. Let L denote the line pass — Solution | TheCATExam