Miguel buys 100 feet of fence to enclose a rectangular area of his backyard so his dog run freely. what is the maximum area, in square feet, he can enclose

The maximum area he can enclose is 625 sq. ft.

In order to maximize area and minimize perimeter, we use dimensions that are as close to equal as possible.  We have 100 ft of fence for a 4-sided figure; 100/4 = 25 ft per side.  

With a length of 25 and a width of 25, we would have an area of 25(25) = 625 sq ft.