To find the answers, we need to follow these steps:
1. Visualize the problem: Draw a diagram of the garden and the walkway around it. This will help us understand the dimensions and relationships between different parts.
2. Define the variables: Let's define the width of the walkway as "w."
a) Perimeter of the walkway along the outer edge:
To find the perimeter, we need to calculate the length of each side of the outer edge.
- The length of the outer edge parallel to the length of the garden is (10ft + 2w).
- The length of the outer edge parallel to the width of the garden is (9ft + 2w).
Therefore, the perimeter of the walkway along the outer edge can be calculated as:
P = 2(10ft + 2w) + 2(9ft + 2w) = 20ft + 4w + 18ft + 4w
P = 38ft + 8w
b) Combined area of the garden and the walkway:
To find the combined area, we need to calculate the area of the garden and add it to the area of the walkway.
- The area of the garden is given by the length multiplied by the width, which is 10ft * 9ft = 90ft².
- The area of the walkway is given by the total area of the outer edge minus the area of the garden. Since the walkway has a uniform width on all sides, the length and width of the walkway rectangle will be (10ft + 2w) and (9ft + 2w) respectively.
Therefore, the area of the walkway can be calculated as:
A_w = (10ft + 2w) * (9ft + 2w)
The combined area of the garden and the walkway is given by:
A_combined = A_garden + A_w
c) Find the combined area when the width of the walkway is 4ft:
Using the formula from part b, substitute w = 4ft into the equation to calculate the combined area.
A_combined = A_garden + (10ft + 2(4ft)) * (9ft + 2(4ft))
Simplify and solve the equation to get the final answer.