Maximizing the Area of a Rectangle
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Part 1: The equation 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?
Part 2: I'm also curious how you know that the one with the largest jury would be the square?
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Solution Summary
The expert examines maximizing the area of a rectangle. Step-by-step solutions to both the parts of the question are provided.
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(Part 1): Length of fencing = Perimeter of the rectangular field = P = 600
Let L = 200 ft.
Then, Area of the field = A = (LP/2) - L^2 = (200 * 600/2) - 200^2 = 20000 ...
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