A farmer has 1600 yards of fencing to enclose a rectangular garden. Express the area A of the rectangle as a function of the width x of the rectangle. What is the domain of A?

A = (800 yd - x) x, [0, 800]

Step-by-step explanation:

The farmer fences in this rectangular garden using 1600 yds of fencing. Using the formula for the perimeter of a rectangle,

P = 2x + 2L, where x is the width and L is the length. Here P = 1600 yd.

Solving for L: 1600 yd = 2x + 2 (L) → 800 yd = x + L → L = 800 yd - x.

The area of the rectangle is A = L·x. Subbing (800 yd - x) for L, we get:

A = (800 yd - x) x. This is the desired formula for the area of the rectangle as a function of x alone. Neither length nor width can be negative, so the domain of this function A is x ≤ 800 yd.