CAT 1995 — QA Question 25
Basics of QuadrilateralsEasy
In the adjoining figure, AC+ AB = 5AD and AC – AD = 8. Then the area of the rectangle ABCD is
Answer & solution
Correct answer: 60
- 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.