A mason has to fit a bathroom with square marble tiles filled of the largest possible size. The size of bathroom is 10 × 8 feet. What would be the size of the tiles in inches that has to be cut and how many such tiles are required?

To determine the size of the largest square marble tiles that can fit in a bathroom measuring 10 feet by 8 feet, we first need to convert the dimensions into inches. Since there are 12 inches in a foot, the dimensions become:

• 10 feet = 10 × 12 = 120 inches
• 8 feet = 8 × 12 = 96 inches

The next step is to find the largest square tile size that can fit both dimensions. This can be done by calculating the greatest common divisor (GCD) of 120 and 96.

The factors of 120 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.

The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.

The largest common factor is 24. Therefore, the size of each tile should be:

Tile Size: 24 inches x 24 inches

Now, to find out how many tiles are needed, we calculate the area of the bathroom and the area of one tile:

• Area of the bathroom = 120 inches × 96 inches = 11,520 square inches
• Area of one tile = 24 inches × 24 inches = 576 square inches

Finally, we divide the total area of the bathroom by the area of one tile to find the number of tiles required:

Number of Tiles Required: 11,520 ÷ 576 = 20

In summary, the size of each tile should be 24 inches, and you will need a total of 20 tiles to fit the bathroom.