Maximum Rectangle Inscribed in a Triangle

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 at the right.


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 rectangle to the area of the original triangle? Prove it!

Hint -- a drawing and some notation.

Further hint (only if desparately needed): Click Here

Extension Problem: Try this.

Presented by Alan Russell (Guest lecturer ).

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