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Maximum Rectangle

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 tex2html_wrap_inline52 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.



Wei-Chi Yang
Wed Oct 30 21:29:01 EST 1996