Mamadou wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn, so he needs no fence on that side. The other three sides will be enclosed with wire fencing. If Mamadou has $850$ feet of fencing, you can find the dimensions that maximize the area of the enclosure.

a$)$ Let $w$ be the width of the enclosure and let $l$ be the length of the enclosure. Write an function for the area $A$ of the enclosure in terms of $w.($HINT first write two equations with $w$ and $l$ and $A.$ Solve for $l$ in one equation and substitute for $l$ in the other$).$

$A(w)=$

b$)$ What width $w$ would maximize the area?

$w=$

$ft$

c$)$ What is the maximum area?

$A=$ square feet