Inscribed rectangle in triangle

Click on point D and move it with the arrow keys. See how the area of the inscribed rectangle changes. The area of the rectangle is traced as a function of the distance AD. What form does the curve representing the area have? When is the area at its maximum? Replace the function x with: 20/3x- 100/27 x^2 and observe how this function fits the trace. Can you find this expression for the area?