The area of the rectangle is {{MATH_16}} In order to be able to use calculus techniques, we have to express the area as a function of a single variable. To this end, we have to express the variable, say {{MATH_17}}, in terms of {{MATH_18}}. How can this be achieved? Recall, we are given the constraint: ``{{CMD_19}} rectangles of perimeter {{MATH_20}}{{CMD_21}}'' If a rectangle has perimeter {{MATH_22}}, then {{MATH_23}}, and we can solve for {{MATH_24}} in terms of {{MATH_25}}, {{MATH_26}} Hence the area of a rectangle of perimeter {{MATH_27}} can be expressed as a function of a single variable, {{MATH_28}}, {{MATH_29}} However, for the side lengths to be physically relevant, we must assume that {{MATH_30}} and {{MATH_31}}. Therefore, the domain of the function {{MATH_32}} is the interval {{MATH_33}}. So, to maximize the area of the rectangle, we have to find the global maximum of the function {{MATH_34}} on the interval {{MATH_35}}. Since the domain of {{MATH_36}} is an open interval, the global maximum (if it exists!