Farmer Joe wants to fence in a rectangular area that has one side bordered by a stream. If he has 80 meters of fencing, what are the dimensions and the maximum area he can enclose? The area of the fenced area can be found using the formula A = lw where l represents the length and w represents the width.

(1st part) Substitute in the formula and simplify to find the function to find the maximum area. Show your work below.

(2nd part) Find the value of x which is the value of the width. Be sure to show each step of your work including simplification.

(3rd part) Substitute into 80 - 2x and simplify to find the value of the length. Show your work below.

(4th part) Substitute x = 20 into the function A = 80x – 2x^2 to find the maximum area. Show your work below.

(5th part) The conclusion is that the dimensions of the fenced area will be ___ meters by ___- meters and the maximum area of the fenced region is square meters.