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CAT 1995 — QA Question 25

Basics of QuadrilateralsEasy
Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

In the adjoining figure, AC+ AB = 5AD and AC – AD = 8. Then the area of the rectangle ABCD is

Answer & solution

  • A

    36

  • B

    50

  • 60

  • D

    Cannot be answered

Solution

Since AD = BC (Opposite sides of a rectangle are equal.)
AB + AC = 5BC and AC – BC = 8 or AC = BC + 8
∴ AB = 4(BC – 2)
By Pythagoras’ Theorem, AB2 + BC2 = AC2
Expressing AB and AC in terms of BC we get, BC = 5.
∴ AB = 12 and AC = 13
So area of the rectangle = 5 × 12 = 60.

CAT 1995 QA Q25: In the adjoining figure, AC+ AB = 5AD and AC – AD = 8. Then the area of the rectangle ABCD is — Solution | TheCATExam