Question 17

The floor of a room is 15m 17cm long and 9m 2cm broad. What is the least number of square tiles required to pave the floor?

Solution

Length of the floor = 15m 17cm = 1517 cm

Width of the floor = 9m 2cm = 902 cm

The overall area of the floor $$=1517\times902$$

To minimise the number of tiles needed to pave the floor, we should calculate the HCF of both the length and width of the floor to determine the side length of each square tile.

$$1517=41\times37$$

$$902=2\times11\times41$$

Thus, HCF(1517,902) = 41

The side length of each square tile is 41 cm.

Number of tiles = Area of Floor / Area of each tile

Number of tiles = $$\dfrac{1517\times902}{41\times41}=37\times22=814$$

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