Question

A rectangular garden measures 15 meters by 8 meters. If a path that is 1 meter wide is built around the garden, what is the total cost of the path if gravel costs $0.05 per square meter?

Answer 1

To find the total cost of the path around the garden, we first need to determine the area of the path.

The garden itself measures 15 meters by 8 meters. The dimensions of the garden with the path included will be wider due to the 1-meter path added all around. This means we will add 2 meters to each dimension (1 meter on each side).

1. **Calculate the dimensions of the garden including the path**:
- Length with path = 15 meters + 2 meters = 17 meters
- Width with path = 8 meters + 2 meters = 10 meters

2. **Calculate the area of the garden with the path**:
\[
\text{Area of the garden with path} = \text{Length} \times \text{Width} = 17 \text{ m} \times 10 \text{ m} = 170 \text{ square meters}
\]

3. **Calculate the area of the garden alone**:
\[
\text{Area of the garden} = 15 \text{ m} \times 8 \text{ m} = 120 \text{ square meters}
\]

4. **Calculate the area of the path**:
\[
\text{Area of the path} = \text{Area of the garden with path} - \text{Area of the garden}
\]
\[
\text{Area of the path} = 170 \text{ square meters} - 120 \text{ square meters} = 50 \text{ square meters}
\]

5. **Calculate the cost of the gravel for the path**:
- Cost per square meter = $0.05
\[
\text{Total cost} = \text{Area of the path} \times \text{Cost per square meter} = 50 \text{ square meters} \times 0.05 \text{ dollars/square meter} = 2.5 \text{ dollars}
\]

Thus, the total cost of the path is **$2.50**.