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Length, Width, Perimeter and Area of a Rectangular Field

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A=(LP)/2-L^2, gives the area of a rectangle of perimeter P and length L. Suppose that you have 600 feet of fencing which you plan to use to fence in a rectangular area of land. Choose any two lengths for a rectangle and find the corresponding area for each using the given equation. Include units and show all calculations. Which of the two lengths that you chose gives a larger area? What is the corresponding width of each of the two rectangles?

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A complete, neat and step-by-step solution is provided, including calculations of area of the field and width.

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Length of fencing = Perimeter of the rectangular field = P = 600

(1) Let L = 200 ft.

Then, Area of the field = A = (LP/2) - L^2 = (200 * 600/2) - 200^2 = ...

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