AMC 8 2008 Problem 17

Ms.Osborne asks each student in her class to draw a rectangle with integer side lengths and a perimeter of $50$ 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? $\textbf{(A)}\ 76 \textbf{(B)}\ 120 \textbf{(C)}\ 128 \textbf{(D)}\ 132 \textbf{(E)}\ 136$