Question

You have a 1800 foot roll of fencing. You are going to enclose a rectangular field. You want to place a row of fence down the middle to divide it into two equal sections. What is the maximum area you can enclose?

Answer 1

The perimeter will be given by

`2x+ 3y = 1800`

Because we need three lengths and two widths.

Hence, we can say

`3y = 1800- 2x`

`y = 600 - 2/3x`

Using `A = L * W`, we get

`A = (600 - 2/3x)x`

`A = 600x - 2/3x^2`

Completing the square to get the vertex:

`A = -2/3(x^2 - 900x + 202500 - 202500)`

`A = -2/3(x^2 - 900x + 202500) + 135000`

`A = -2/3(x - 450)^2 + 135000`

So the maximum area is `135000` square feet and the dimensions that will make it are `450` by `300`.

Hopefully this helps!