# You have 76 feet of fencing to fence an area in the yard. The area must have right angle corners. You can use the side of your home which is 85 feet long. What is the largest are you can fence in?

May 6, 2016

Maximum area = 722 sq ft

#### Explanation:

We are working with a rectangle. The one side can be 85 ft long, but this is longer than the entire length of fencing available, so we will obviously only use part of the wall, and the fencing will be used for three sides of the rectangle.

Let one side be $x$. The other sides will be $x$ and $\left(76 - 2 x\right)$

$A r e a = l \times b = x \left(76 - 2 x\right)$

$A r e a = 76 x - 2 {x}^{2}$

$\frac{\mathrm{dA}}{\mathrm{dx}} = 76 - 4 x$ $\textcolor{w h i t e}{\times \times \times}$ for a max $\frac{\mathrm{dA}}{\mathrm{dx}} = 0$

$76 - 4 x = 0$
$76 = 4 x$
$x = 19$

The dimensions are therefore 38ft by 19ft, giving an area of 722sq ft