Total fencing = 500 feet
x + x + x + x + y + y = 500
2y + 4x = 500
Y + 2x = 250
Y = 250 – 2x
Now, area,
A = (x) (y)
A = (x) (250 – 2x)
A = 250x – 2x^2
dA/dx = 0 for maximum area
d/dx (250x – 2x^2) = 0
250 – 4x = 0
4x = 250
X = 62.5
Y = 250 – 2 (62.5) = 12.5
Hence, the dimension of the rectangular area are :
Length y = 125 feet
Width w = 62.5 feet
