Apark ranger has 32 feet of fencing to fence four sides of a rectangular recycling site

The complete question is as following.
A park ranger has 32 feet of fencing to fence four sides of a rectangular recycling site. What is the greatest area of recycling site that the ranger can fence? Explain how you know.

Solution:
Let the dimension of the park are x , y
∴ 2x + 2y = 32
   y = 16 - x

Area = A = xy = x (32 - x) = 16x - x²
Differentiating the area with respect to x and equating to zero
∴ dA/dx = 16 - 2x = 0
Solve for x
∴ x = 8  and   y = 8

∴ The dimension of the park = 8 , 8 feet
And the greatest area = 8 * 8 = 64 ft²