The perimeter of a rectangle is 60 meters. What are the possible lengths of any of the rectangle’s sides if its area exceeds 216 square meters?

Let the rectangle’s sides be x and 30 − x, since 2(x + y) = 60 gives x + y = 30. Its area exceeds 216 when x(30 − x) > 216, or (x − 12)(x − 18) < 0. Thus x must be strictly between 12 and 18 meters, matching (12, 18).

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