What is the largest rectangular area that can be enclosed with 100 feet of fencing? What is the dimension of the rectangle?
First we recall the area of a rectangle = base 
height. Suppose
one side of the rectangle is x then the other side should be
(100 - 2x)/2 Therefore, the area function A(x) = x[(100-2x)/2]
.
The maximum occurs at x = -b/(2a) = 25 feet and A(25)=625
square feet. The dimension of this rectangle is 25 by 25,
which is a square.