Question

The length and breadth of a rectangular field are 165m and 120m. If the field is to be paved with identical square tiles of maximum size, then the length of the side of the tiles is

• A. 10m
• B. 11m
• C. 16m
• D. 15m

Hint:

Maximum square tile size equals the HCF of the two dimensions.

Answer 1

The Correct Option is D

Concept: Largest square tile side = HCF (GCD) of length and breadth. Explanation: Find HCF of 165 and 120. Prime factorization: \[ 165 = 3 \times 5 \times 11 \] \[ 120 = 2^3 \times 3 \times 5 \] Common factors = $3 \times 5 = 15$