Question

Craig has 60 feet of fencing with which to make a rectangular garden area. One side of the rectangular garden will be the side of the Craig's house. Find the length and width for a maximum garden area.

What are the dimensions? And area?

Answer 1

Answer: 15 by 30 feet, area is 450 square feet

Explanation:

Let the length be l and the width be w.

The perimeter is l+2w (since one side is against the house)

We also know the area is lw.

Since
`l+2w=60 \implies l=60-2w`, the area is the same as
`w(60-2w)`.

The zeros of this area function are 0 and 30, so the value for which it is maximized is halfway between these values - 15.

If w=15, then l=30.

Therefore, the area is 450 square feet.