Question

A floor of a room is 9 m long and 6 m wide. Find the largest size of the square tile that can be used to tile the floor without cutting any tile

Answer 1

Given,

The length of the floor of the room is 9 metres.

The width of the floor of the room is 6 metres.

To find,

The size of largest square tile which can be used to tile the floor without cutting any tile.

Solution,

First of all, we need to calculate the area of the floor of the room by using the following mathematical formula,

area of the floor of the room = length of the floor of the room × width of the floor of the room = 9×6 = 54 m²

Now,the tiles cannot be broken. So,the total number of tiles will be a whole number.

So,we need to divide the area of floor with positive whole numbers (starting from 1). The first quotient which becomes a perfect square,will be the length of one side of the tile.

So,

54 ÷ 1 = 54 (not a perfect square)

54÷ 2 = 27 (not a perfect square)

54 ÷ 3 = 18 (not a perfect square)

54 ÷ 4 = 13.5 (not a perfect square)

54 ÷ 5 = 10.8 (not a perfect square)

54 ÷ 6 = 9 (perfect square)

One side of the tile = √9 = 3 metres

Hence,the length of the one side of the biggest possible tile will be 3 metres.