Hi Billy,

Suppose the garden is L feet long and W feet wide. The perimeter is then

L + W + L + W = 38 feet

so

L + W = 19 feet

or

L = 19 - W feet.                (1)

The area of a rectangle is the length times the width so

area = L × W.                      (2)

Substitute equation (1) into equation (2) and you will have the area expressed as a function of W.

If you are studying calculus you can now use calculus to maximize this function. If you are studying algebra and you know how to maximize a quadratic you can proceed that way.

I hope this helps,
Penny