Determine all real numbers a 0 for which there exists a nonnegative continuous function (x) defined on 0, a with the property that the region R (x, y) 0 x a, 0 y (x) has perimeter k units and area k square units for some real number k

Question: Determine all real numbers a > 0 for which there exists a nonnegative continuous function (x) defined on [0, a] with the property that the

Determine all real numbers a > 0 for which there exists a nonnegative continuous function ƒ(x) defined on [0, a] with the property that the region R = {(x, y); 0 ≤ x ≤ a, 0 ≤ y ≤ ƒ(x)} has perimeter k units and area k square
units for some real number k.

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