The least number of square tiles required to pave the ceiling is (B) 814.
To determine the least number of square tiles needed to pave a room, follow these steps:
Step 1: Convert all dimensions to a single unit (centimeters).- The room's length is 15 meters and 17 centimeters.
- Since 1 meter equals 100 centimeters, the length in centimeters is (15 * 100) + 17 = 1517 cm.
- The room's breadth is 9 meters and 2 centimeters.
- In centimeters, this is (9 * 100) + 2 = 902 cm.
The side length of each square tile must be the HCF of the room's length and breadth to find the least number of tiles.
- First, find the prime factorization of 1517 and 902:
- 1517 = 37 × 41
- 902 = 2 × 11 × 41
- The HCF of 1517 and 902 is 41. Therefore, the side of each square tile will be 41 cm.
- Number of tiles along the length = (Length of room) / (Side of tile) = 1517 cm / 41 cm = 37 tiles.
- Number of tiles along the breadth = (Breadth of room) / (Side of tile) = 902 cm / 41 cm = 22 tiles.
The total number of square tiles required is the product of the number of tiles along the length and the number of tiles along the breadth:
- Total tiles = 37 × 22 = 814 tiles.
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