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23 February, 07:44

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?

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  1. 23 February, 10:47
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    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.
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