You have a 500 foot roll of fencing and a large field. You want to construct a rectangular playgorund area. What are the dimensions of the largest such yard? What is the largest area?

Question

Application of quadratic function. Its hard for me to analyze the problem so i need some help.

Answer 1

The perimeter of the rectangle is 2(L+W) where L and W are length and width. So L+W=250'. W=250-L.

Area=L(250-L). This area is maximum when L=125, area=125^2=15625 sq ft. (rectangle is a square).

To prove this let L=125+a and W=125-a. Perimeter=2(125+a+125-a)=500.

Area=125^2-a^2, which is always <125^2 except when a=0. So the maximum area is 125^2.