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CAT 2003 Slot 1 — QA Question 35

Height & DistanceEasy
Passage / Data

Each question is followed by two statements, A and B. Answer each question using the following instructions

Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.

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

  • A

    2b2 = h2

  • 2h2 = b2

  • C

    3b2 = 2h2

  • D

    3h2 = 2b2

Solution

OP = h and AB = b

Now, OA = AC2=b22=b2

OP is a perpendicular tower at the centre O of the square.

In ∆PAB, PA = PB

∴ ∠PAB = ∠PBA = ∠APB = 60°

∴ ∆PAB is an equilateral triangle.

∴ AP = b

In the right-angled ∆AOP, we have,

AP2 = OP2 + OA2

∴ b2 = h2 + b22

∴ 2h2 = b2

Hence, option (b).

CAT 2003 Slot 1 QA Q35: A vertical tower OP stands at the centre O of a square ABCD. Let h and b denote the lengths OP and AB respecti — Solution | TheCATExam