Inscribed Rectangle

Consider the four vertices of a rectangle. To have a rectangle inscribed in a triangle, two of the rectangle’s vertices must lie on the same side of the triangle. Here are some examples:

Given a triangle, construct the inscribed rectangle with maximum area. Is there a “maximum rectangle” for each side of the triangle?

What is the relation of the area of the maximum rectangle to the area of the original triangle? Prove it!

Hint – a drawing and some notation.

Further hint (only if desperately needed): Click Here


Extension Problem: Try this.

Presented by Alan Russell (Guest lecturer).