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?

Answer: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.