The length of a rectangular garden is 8 feet longer than it's width. The garden is surrounded by a sidewalk that is 4 feet wide and has a area of 320 square feet. Find the dimensions of the garden.

The length = 20

The width = 12

Explanation:

Let the Length of the garden be L and the Width W

Therefore the area of the garden = L*W

But we know that L = W + 8

Therefore the area of the garden can be expressed as W * (W + 8)

When the brackets are expanded this equals W^2 + 8W

The area of the recctangle which includes the path and garden will have a length of L + 8 (ie the length of the garden + 4 feet at the top and 4 feet at the bottom)

The width will be W + 8 (width of garden + 4 feet at the left and 4 feet at the right)

Therefore the area will be (W + 8) * (L + 8)

Once again we know that L = W + 8

Therefore the area of the path/garden = (W + 8) (W + 8 + 8)

= (W + 8) (W + 16)

=W^2 + 24W + 128

We know that the path alone has an area of 320 square feet. Therefore if we subtract the area of the garden (W^2 + 8W) from the area of the path/garden the area left is the area of the path only

Therefore W^2 + 24W + 128 - (W^2 + 8W) = 320

W^2 + 24W + 128 - W^2 - 8W = 320

Simplify

16W + 128 = 320

Subtract 128 from both sides of the equation

16W = 192

divide both sides of the equation by 16

W = 12

As L = W + 8

L = 12 + 8 = 20