You are going to build a rectangular pen with 200 feet of fencing. Give the maximum possible area.

Question

You are going to build a rectangular pen with 200 feet of fencing. Give the maximum possible area.

Answer 1

This is a simple calculus problem but it can be solved without calculus, as follows:

 

let L=length of the pen and W = width

2(L + W) = 200 => L + W = 100 => L = 100 - W

 

Let A = area of the pen

A = L*W = 100W - W²

 

Sketch this parabola which has a positive maximum which occurs at W = 100/2

(Note the maximum of the parabola Ax² + Bx + C occurs at x=-B/2A)

 

This means the area is maximum when W = 50, in other words the maximum area occurs when the rectangle is a square!