Largest Square Marble Tile for a Bathroom of 10 ft by 8 ft

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: A mason has to fit a bathroom with square marble tiles of the largest possible size. The size of the bathroom is 10 ft by 8 ft. What would be the size in inches of the tile required and how many such tiles are required?

Step 1: Convert Dimensions into Inches

Length of bathroom = 10 ft = 10 × 12 = 120 inches

Breadth of bathroom = 8 ft = 8 × 12 = 96 inches

Step 2: Find the Largest Possible Size of Square Tile

The side of the largest square tile is the HCF of 120 and 96.

Using Euclid’s division algorithm:

120 = 96 × 1 + 24

96 = 24 × 4 + 0

∴ HCF (120, 96) = 24

So, the required size of each square tile is 24 inches × 24 inches.

Step 3: Find the Number of Tiles Required

Number of tiles along the length = 120 ÷ 24 = 5

Number of tiles along the breadth = 96 ÷ 24 = 4

Total number of tiles = 5 × 4 = 20

Final Answer

∴ The size of each square tile is 24 inches × 24 inches and the total number of tiles required is 20.

Conclusion

Thus, by using Euclid’s division algorithm, we find that the largest possible square tile has a side of 24 inches and exactly 20 such tiles are needed to fit the bathroom.