CAT 2003 Slot 1 — QA Question 35
Height & DistanceEasy
A vertical tower OP stands at the centre O of a square ABCD. Let h and b denote the lengths OP and AB respectively. Suppose ∠APB = 60°, then the relationship between h and b can be expressed as
Answer & solution
Correct answer: 2 h 2 = b 2
- A
2b2 = h2
2h2 = b2
- C
3b2 = 2h2
- D
3h2 = 2b2
Solution
OP = h and AB = b
Now, OA =
OP is a perpendicular tower at the centre O of the square.
In âPAB, PA = PB
∴ ∠PAB = ∠PBA = ∠APB = 60°
∴ âPAB is an equilateral triangle.
∴ AP = b
In the right-angled âAOP, we have,
AP2 = OP2 + OA2
∴ b2 = h2 +
∴ 2h2 = b2
Hence, option (b).