2 The side length of a square tile is 200 mm and the side length of a square floor is \( 2,4 \mathrm{~m} \). a Express the side lengths as a ratio. b Express the area of the floor and the area of one tile as a ratio. c How many tiles are required to cover the floor?

To find the ratio of the side lengths, we first need to express them in the same unit. The side length of the tile is 200 mm, which is 0.2 m. The side length of the floor is 2.4 m. The ratio of the side lengths can be found by dividing each by its simplest form: \[ \frac{0.2}{2.4} = \frac{1}{12} \] So, the ratio of the side lengths is \( 1:12 \). Next, we calculate the areas. The area of one tile is: \[ \text{Area}_{\text{tile}} = 0.2 \, \text{m} \times 0.2 \, \text{m} = 0.04 \, \text{m}^2 \] The area of the floor is: \[ \text{Area}_{\text{floor}} = 2.4 \, \text{m} \times 2.4 \, \text{m} = 5.76 \, \text{m}^2 \] The ratio of the areas is: \[ \frac{0.04}{5.76} = \frac{1}{144} \] So, the ratio of the areas is \( 1:144 \). To determine how many tiles are required to cover the floor, we divide the area of the floor by the area of one tile: \[ \text{Number of tiles} = \frac{5.76}{0.04} = 144 \] Hence, a total of 144 tiles is required to cover the floor.