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geometry junior

Problem

Ms.Osborne asks each student in her class to draw a rectangle with integer side lengths and a perimeter of units. All of her students calculate the area of the rectangle they draw. What is the difference between the largest and smallest possible areas of the rectangles?
(A)
(B)
(C)
(D)
Solution
A rectangle's area is maximized when its length and width are equivalent, or the two side lengths are closest together in this case with integer lengths. This occurs with the sides . Likewise, the area is smallest when the side lengths have the greatest difference, which is . The difference in area is .
Final answer
D