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

To solve this problem, we need to determine the size of the largest square tile that can exactly fit into both the length and breadth of the rectangular field. This can be done by finding the greatest common divisor (GCD) of the length and breadth of the field.

1. Given the dimensions of the rectangular field:
   • Length = 165 m
   • Breadth = 120 m
2. We need to find the GCD of 165 and 120 to determine the maximum size of the square tile.
3. Using the Euclidean algorithm:
   • First, divide 165 by 120: \[ 165 \div 120 = 1 \quad \text{remainder} = 45 \]
   • Next, divide 120 by the remainder (45): \[ 120 \div 45 = 2 \quad \text{remainder} = 30 \]
   • Then, divide 45 by the new remainder (30): \[ 45 \div 30 = 1 \quad \text{remainder} = 15 \]
   • Finally, divide 30 by the latest remainder (15): \[ 30 \div 15 = 2 \quad \text{remainder} = 0 \]
4. Since the remainder is 0, the GCD is the last non-zero remainder, which is 15.
5. Thus, the maximum size of the square tile that can pave the entire field is 15 meters.

Therefore, the correct answer is 15m.