A rectangular floor of a a room measures 5 .4m long and 4.2m wide. The room is to be covered with square tiles. Calculate the minimum number of squares tiles can be used to cover the floor ?

To find the minimum number of square tiles needed to cover the floor, we need to calculate the area of the floor and then divide it by the area of each square tile.

Area of the floor = length x width
Area of the floor = 5.4m x 4.2m
Area of the floor = 22.68 square meters

Let's assume each square tile has a side length of x meters.

Area of each square tile = x^2

To find the minimum number of square tiles needed, we divide the area of the floor by the area of each square tile:

Number of square tiles = Area of the floor / Area of each square tile
Number of square tiles = 22.68 / x^2

Since the side length of each square tile is the same, we can set x = side length of each square tile.

To minimize the number of square tiles, we want to find the largest possible square tile that can fit into the floor area. In this case, the largest possible square tile would be the greatest common divisor (GCD) of the length and width of the floor.

GCD(5.4, 4.2) = 1.2

Therefore, the minimum number of square tiles that can be used to cover the floor is:

Number of square tiles = 22.68 / 1.2^2
Number of square tiles = 22.68 / 1.44
Number of square tiles ≈ 15.75

Since we can't have a fraction of a tile, we would need to round up to the nearest whole number. Therefore, the minimum number of square tiles needed to cover the floor is 16.

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