A piece of paper has the precise shape of a triangle with the three side lengths AB, AC and BC being respectively 2, 4/3 and √10/3. The paper is folded along a line perpendicular to the side AB.

Determine the largest possible overlapped area.

A quick sketch on geometer's sketchpad lead me to a solution of

.2979218

playing a bit with this value leads me to sqrt(15)/13

I will try for some kind of proof later.  But this feels like a calculus problem.

Posted by Jer on 2014-02-12 08:44:40