Maximum Area

[Stuckonproblems]

A farmer must use 100 feet of fencing and an existing 20 feet side of a shed to enclose a rectangular pen. Find the dimensions of x and y of the enclosure resulting in maximum area.

____20 ft______
l_____________ l
l______SHED___l
l_____________l
l_____________l_______
l____________________l
l____________________l y
l____________________l
l____________________l
l____________________l
​___________x

I'm stuck on this problem could you guys correct my area and then show me the steps of how to find the maximum area. Thanks

Area = (x-20)x*y ?

 

[Stuckonproblems]

So after you get:

A=60x-x²

Then after that you set Area equal to zero.

0=60x-x²
x=60

Plug it back into perimeter equation to solve for y:

100=2(60)+2y-20
0=2y
0=y

How can this be? Or did I do something wrong?