Question

Isaac wants to cover his bedroom floor that measures 1.2 m by 2 m with identical square tiles. Given that he uses only whole tiles, fin the largest number of tiles need to cover the floor.

Answer 1

The area of the bedroom floor is 1.2 m * 2 m = 2.4 square meters.
Since the tiles are identical squares, they have the same length and width.
Let's assume the length of one tile is x.
The area of one tile is x * x = x^2 square meters.
To cover the entire floor, we need to divide the area of the floor by the area of one tile.
The number of tiles needed is 2.4 / x^2.
Since Isaac wants to use only whole tiles, the number of tiles needed must be a positive integer.
Therefore, we need to find the largest perfect square that is a factor of 2.4.
The prime factorization of 2.4 = 2 * 2 * 2 * 3 * 5 * 5 * 5.
The largest perfect square factor of 2.4 is 2 * 2 * 3 = 12.
Therefore, Isaac needs 12 tiles to cover his bedroom floor.