**Q:** You have 128 feet of fencing to fence a rectangular area. Find the largest possible area to enclose this amount.

**A:** The perimeter of the space will be 128=2w+2L, where w=width and L=length

Isolate for L: L=64-w

The formula for the area of the rectangle is A=w*L. Substitute L=64-w into the area formula so that we only have one variable, w.

We want to maximize A, so we need to graph A vs w, by completing the square.

Graph this to see that the maximum area of occurs when **w=32 ft**. This makes sense, as it is a **32 x 32** square. A square gives the Max area.

Here’s a link to a graph of the function. Note that area is the y axis, and width is the x axis.

## Follow Us!