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

Question

Answer

Size of bathroom given=10×8 feet,
or, area of bathroom=(10×12)×(8×12)(1feet=12inches),
HCF(120,96)=24= side of 1square tile,
number of tiles required= area of bathroom/ area of tile=120×96/24×24=20 tiles

Answer

Area of bathroom = 10 x 8 = 80

So, 80 must be a multiple of the area of the required square tiles. Here only 16 and 4 are the only possibilities since area of square must be a perfect square.

- If you take area of the tile as 16 (4 ft x 4 ft) then you need 5 such tiles to get a total area of 80. But if you want them to be arranged in a 10 ft x 8 ft rectangle, four tiles can be kept straight away but the last tile need be divided into to equal rectangles of dimensions 2 ft x 4 ft which against the question since every tile must be a square.

- So, you have to only choose the tile whose area is 4 (2 ft x 2 ft) and you need 20 such tiles to get a total area of 80. They can be arranged into 5 rows and 4 columns to form a 10 ft x 8 ft rectangle.

Answer

Maximizing Tile Size for a Bathroom

Problem Statement

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

Solution

Step 1: Find the Area of the Bathroom

To determine the total area of the bathroom, we need to multiply the length and width of the bathroom:

Area of Bathroom = Length x Width

Area of Bathroom = 10ft x 8ft = 80 sq. ft.

Step 2: Determine the Largest Tile Size

To determine the largest tile size that can be used, we need to find a square number that can be evenly divided into the area of the bathroom. This will ensure that the tiles will fit without any gaps.

The largest square number that can be evenly divided into 80 sq. ft. is 16 sq. ft. This means that each tile must cover an area of 16 sq. ft.

Step 3: Convert to Inches

We need to convert the size of the tile from square feet to square inches, as this is the standard unit for tile size. There are 144 square inches in a square foot.

16 sq. ft. = 16 x 144 sq. in. = 2,304 sq. in.

Therefore, each tile must cover an area of 2,304 sq. in.

Step 4: Determine the Tile Size in Inches

To determine the size of each tile in inches, we need to find the square root of 2,304 sq. in.

Tile Size = √2,304 sq. in. = 48 in.

Therefore, each tile must be 48 inches on each side.

Step 5: Determine the Number of Tiles Required

To determine the number of tiles required, we need to divide the area of the bathroom by the area of each tile.

Number of Tiles = Area of Bathroom / Area of Each Tile

Number of Tiles = 80 sq. ft. / 16 sq. ft. = 5

Therefore, we need 5 tiles to cover the entire bathroom.

Conclusion

The mason should use square marble tiles that are 48 inches on each side, and 5 tiles are required to cover the entire bathroom.

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