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,
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.