A farmer has 64 feet of fence to enclose a rectangular vegetable garden which dimensions will result in the biggest

Perimeter (P) = 2L + 2w

64 = 2L + 2w

64 - 2L = 2w

32 - L = w

Area (A) = L x w

= L x (32 - L)

= 32L - L²

To find maximum area, calculate the derivative and set it equal to zero.

A' = 32 - 2L

0 = 32 - 2L

2L = 32

L = 16

Substitute L to solve for y: 32 - L = w → 32 - 16 = w → 16 = w

The maximum area will be 16 ft x 16 ft = 256 ft²