(4 A swimming pool was built on a rectangular plot of land. The plot of land measured 60 m by 35 m . A 5 m wide path was left around the pool. (a) What was the perimeter of the pool? (b) What was the area of the path?

To solve the problem, we first need to determine the dimensions of the swimming pool itself, given that there is a 5 m wide path around it. ### Step 1: Calculate the dimensions of the pool The dimensions of the rectangular plot of land are: - Length = 60 m - Width = 35 m Since there is a 5 m wide path around the pool, we need to subtract twice the width of the path (5 m on each side) from both the length and the width of the plot to find the dimensions of the pool. **Length of the pool:** \[ \text{Length of the pool} = 60 \, \text{m} - 2 \times 5 \, \text{m} = 60 \, \text{m} - 10 \, \text{m} = 50 \, \text{m} \] **Width of the pool:** \[ \text{Width of the pool} = 35 \, \text{m} - 2 \times 5 \, \text{m} = 35 \, \text{m} - 10 \, \text{m} = 25 \, \text{m} \] ### Step 2: Calculate the perimeter of the pool The perimeter \( P \) of a rectangle is given by the formula: \[ P = 2 \times (\text{Length} + \text{Width}) \] Substituting the dimensions of the pool: \[ P = 2 \times (50 \, \text{m} + 25 \, \text{m}) = 2 \times 75 \, \text{m} = 150 \, \text{m} \] ### Step 3: Calculate the area of the path To find the area of the path, we first calculate the area of the entire plot and then subtract the area of the pool. **Area of the plot:** \[ \text{Area of the plot} = \text{Length} \times \text{Width} = 60 \, \text{m} \times 35 \, \text{m} = 2100 \, \text{m}^2 \] **Area of the pool:** \[ \text{Area of the pool} = \text{Length} \times \text{Width} = 50 \, \text{m} \times 25 \, \text{m} = 1250 \, \text{m}^2 \] **Area of the path:** \[ \text{Area of the path} = \text{Area of the plot} - \text{Area of the pool} = 2100 \, \text{m}^2 - 1250 \, \text{m}^2 = 850 \, \text{m}^2 \] ### Final Answers (a) The perimeter of the pool is **150 m**. (b) The area of the path is **850 m²**.