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.

The greatest area he can fence is 64 ft².

In order to maximize area and minimize perimeter, we use dimensions that are as close to equivalent as possible.  32 feet of fence for 4 sides gives us 8 feet of fence per side.  We would have a square whose side length is 8; the area would be 8*8 = 64.