The area is equal to length times width. [tex]A=lw[/tex]
The perimeter is equal to twice the sum of the length and the width. [tex]p=2l+2w[/tex]
We know that the perimeter is 450 meters, the length is [tex]450-2x[/tex] meters, and the width is [tex]x[/tex] meters.
To maximize the area, we find the global maximum of the function [tex]a(x)=x(450-2x)[/tex]. The easiest way is to use the formula for the vertex, [tex]x= \dfrac{-b}{2a} = 450/4 = 112.5 \ m[/tex], and [tex]f( \dfrac{-b}{2a})=f(112.5)=25,312.5 \ m^2[/tex].
I realize it sounds like a big number, but the largest area that can be enclosed is 25,312.5 m^2 (if I did this correctly!).
