Given is ∆ ABC. Rectangle DEFG is inscribed in ∆ ABC. Find the rectangle with maximum area.
Drag point D on segment AB to construct several inscribed rectangles.
1. Click on "Test by folding" and drag the green points to fold the blue parts of the triangle over the inscribed rectangle.

Move Point D on AB and observe for what position of D the reflected triangles will not overlap.

What should be the side of the rectangle with maximum area?

What is the maximum area of the rectangle as a fraction of the area of the triangle?

2. Click on show/hide axes to see the graph of the area of the rectangle DEFG as a function of the side , when D changes between A and H.