A farmer has 64 feet of fence to enclose a rectangular vegetable garden. which dimensions would result in the biggest area for this garden

The dimensions that would result to maximum area will be found as follows:

let the length be x, the width will be 32-x

thus the area will be given by:

P (x) = x (32-x) = 32x-x²

At maximum area:

dP' (x) = 0

from the expression:

P' (x) = 32-2x=0

solving for x

32=2x

x=16 inches

thus the dimensions that will result in maximum are is length=16 inches and width=16 inches