Question

A rectangular garden has a walkway around it. The area of the garden is 6(4.5x + 2.5). The combined area of the garden

and the walkway is 6.5(6x + 6). Find the area of the walkway around the garden as the sum of two terms.

Answer 1

2w^2.

Explanation:

Let "w" be the width of the walkway. Then, the length of the garden is 6.5(6x + 6) - 2w and the width of the garden is 6.5(6x + 6) - 2w.

The area of the garden is 6(4.5x + 2.5) = 6 * 4.5 * x + 6 * 2.5 = 27x + 15

The area of the garden and walkway is (6.5(6x + 6) - 2w)^2 = 27x + 15 + 2w^2

Equating the two expressions for the area of the garden:

27x + 15 = 27x + 15 + 2w^2

Thus, the area of the walkway is: