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?