Every triangle has a square which is the maximum size square which can be inscribed in the triangle. For most triangles there is only one way to do so. For an equilateral triangle there are three ways to inscribe the square - one for each side.

The equilateral is not the only triangle with that property; there is one other triangle whose maximum inscribed square can be placed on all three sides. Determine the dimensions of that triangle! (Assume the shortest edge is 1 unit.)

(In reply to re: My solution by broll)

I was only being generous to myself.  I filled quite a few sheets of paper with perspiration before sleeping on the problem.  The inspiration came while I was asleep.

And I still had a lot of work to do this morning. 

In retrospect this is a great D4 problem.

Posted by Jer on 2016-02-27 22:35:46