PROBLEM: 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:
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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