The length of the 3 sides
has a total dimension of 720 ft. One dimension, the length l, only has one side
enclosed. The other dimension, the width w, has 2 sides enclosed. So,
720 ft = l + 2w
Rearranging in terms of l:
l = 720 - 2w
Then the area equals
length times width, or:
A = (720-2w)(w) = 720w - 2w^2
To get the maximum area, we take the derivative of the Area
equation and set the derivative equal to 0: dA/dw = 0
dA/dw = 720 - 4w = 0
720 - 4w = 0
4w = 720
w = 180 ft
Calculating for l:
l = 720 – 2w
l = 720 – 2(180)
l = 360 ft
Therefore to get the maximum enclosed area, the width (2 sides) should be 180 ft while the length (1 side) is 360 ft.
