# 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 that has to be cut and how many such tiles are required?

Given:  The size of the bathroom is 10 ft. by 8 ft.

To find: the size in inches of the tile required that has to be cut and how many such tiles are required?

Solution:

To find the largest size of tile, we should find HCF of 10 and 8

Prime factors of 10 = 2 × 5

Prime factors of 8 = 2 × 2 × 2

Therefore HCF of 10 and 8 is: 2 ft

Since i ft = 12 inches

Therefore the largest size of tile is: 2 × 12 inches = 24 inches

Area of bathroom = length of bathroom × breadth of bathroom

= 10 × 8

= 80 sq. ft

Area of 1 tile = length of tile × breadth of tile

= 2 × 2

= 4 sq. ft

Number of tiles = = = 20 tiles

NOTE: Always find the HCF of the given values to find their maximum.

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