Final answer:
The area of a rectangular yard enclosed by 120 feet of a fence is determined by the dimensions of the rectangle. If the yard is a square, the area would be 900 square feet, but other rectangular dimensions could have different areas.
Step-by-step explanation:
If 120 feet of fence is to be used to enclose a rectangular yard, the resulting area of the fenced yard is determined by first defining the length and width of the rectangle and then calculating the area. Let's say the length of the rectangle is L feet and the width is W feet. The perimeter P is given by P = 2L + 2W. Since we have 120 feet of fence, our equation is 2L + 2W = 120. To express the area A of the rectangle, we use the formula A = L × W.
To maximize the area enclosed by a given fence length, the yard should be square, meaning the length and width should be equal. For a square, L = W, our equation 2L + 2W = 120 becomes 4L = 120, so each side L would be 30 feet and the area would be 900 square feet. However, without further constraints, there are infinitely many rectangle dimensions that could use 120 feet of fence while producing different areas.