The length of a rectangular garden is 5 feet longer than its width.

Question

The length of a rectangular garden is 5 feet longer than its width. The garden is surrounded by a 2-foot wide sidewalk. The sidewalk has an area of 76 square feet. Find the dimensions of the garden.

Answer 1

Use w for width and (w+5) for length.

Since the garden is surrounded by the 2 foot wide sidewalk, the length of the garden + sidewalk will be (w+5)+4 (sidewalk on both sides so 2 + 2 = 4), and the width fo the garden + sidewalk will be (w + 4).

After simplifying, for garden + sidewalk, the length is w+9 and width will be w+4.

For just the garden, length is 2+5 and width is w.

Since we are given the area of the sidewalk (which would be the area of the garden subtracted from the area of the garden + sidewalk), we can write this equation:

(w+9)(w+4) - (w+5)(w) = 76

w^2 + 4w + 9w + 36 - w^2 - 5w = 76

8w + 36 = 76

8w = 40

w=5

Plug that in to find the length:

l = w+5

l = 10