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?

Let's solve the problem step by step. **Given:** - Side length of one square tile = 200 mm - Side length of the square floor = 2.4 m **Note:** To express ratios effectively, it's best to convert both measurements to the same unit. We'll convert meters to millimeters since 1 m = 1000 mm. \[ 2.4\, \text{m} = 2.4 \times 1000 = 2400\, \text{mm} \] --- ### **a. Express the side lengths as a ratio** **Tile side length:** 200 mm **Floor side length:** 2400 mm The ratio of the side lengths is: \[ \text{Tile} : \text{Floor} = 200\, \text{mm} : 2400\, \text{mm} \] Simplify the ratio by dividing both terms by 200: \[ 200 : 2400 = \frac{200}{200} : \frac{2400}{200} = 1 : 12 \] **Answer:** The ratio of the side lengths is \(1 : 12\). --- ### **b. Express the area of the floor and the area of one tile as a ratio** First, calculate the areas. **Area of one tile:** \[ \text{Area}_{\text{tile}} = (\text{Side length})^2 = 200^2 = 40,\!000\, \text{mm}^2 \] **Area of the floor:** \[ \text{Area}_{\text{floor}} = (\text{Side length})^2 = 2400^2 = 5,\!760,\!000\, \text{mm}^2 \] Now, form the ratio of the floor area to the tile area: \[ \text{Floor Area} : \text{Tile Area} = 5,\!760,\!000\, \text{mm}^2 : 40,\!000\, \text{mm}^2 \] Simplify the ratio by dividing both terms by 40,000: \[ \frac{5,\!760,\!000}{40,\!000} : \frac{40,\!000}{40,\!000} = 144 : 1 \] **Answer:** The ratio of the floor area to one tile area is \(144 : 1\). --- ### **c. How many tiles are required to cover the floor?** From part **b**, we've established that: \[ \text{Floor Area} : \text{Tile Area} = 144 : 1 \] This means that 144 tiles are required to cover the entire floor. **Answer:** **144 tiles** are needed to cover the floor.