Afarmer 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