Question

Isaac wants to cover his bedroom floor that measure 1.2 m by 2 m with identical square tiles. Given that he uses only whole tiles, find the largest possible length, in cm, of the side of each tile,

Answer 1

To cover the bedroom floor, Isaac needs square tiles that can fit evenly into the dimensions of the floor. The length of the tiles must evenly divide both 1.2 m and 2 m.

To find the largest possible length, we need to find the greatest common divisor (GCD) of 1.2 m and 2 m.

Converting 1.2 m and 2 m to centimeters:
1.2 m = 120 cm
2 m = 200 cm

Now, we find the GCD of 120 cm and 200 cm:
120 = 2^3 * 3 * 5
200 = 2^3 * 5^2

The common factors are 2^3 * 5 = 40.

Therefore, the largest possible length of each side of the tile is 40 cm.