Final answer:
To maximize the area of a rectangle with a given perimeter, solve for the dimensions using optimization techniques in calculus.
Explanation:
To find the dimensions of a rectangle that maximize its area given a perimeter, we first determine the expressions for the length and width. Let the length of the rectangle be represented by x and the width by y. Since the perimeter is given as 40 m, 2x + 2y = 40, which simplifies to x + y = 20. To maximize the area A, we need to differentiate the area formula A = xy and find critical points.
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