Wendy has 180 feet of fencing. She needs to enclose a rectangular space with an area that is ten times its perimeter. If she uses up all her fencing material, how many feet is the largest side of the enclosure?

Okay well we know she will use all of her fencing, so the total will be 180 like so.

180 = p.

(since it will only cover the perimeter of the rectangular area)

and let's call perimeter p and area a.

we know that A = 10p.

Also, we know P = a/10.

Since 180 = p, and p = a/10, we can set them equal to each other to solve for a.

180 = a/10

1800 = a. The area is 1,800 square feet.

(Remember, we know the perimeter is 180 feet).

Work from earlier:

P=2 (b + h) = 180 A=bh=10∗P=10∗180=1800 b+h=90 b∗h=1800

So the area is 1800 and the perimeter is 90.

So, we know that 90 = 2 (40 + 5)

So the longer side will be 40 feet.