An equilateral triangle PQR is drawn inside a unit square LQST such that Q corresponds to the common vertex of the square and the triangle.

Determine the maximum possible area of the triangle PQR.

(In reply to Solution by Bractals)

Expecting to find help for a shortcut on Wolfram Mathworld (mathworld.wolfram.com), I found that this same problem was presented and solved.

Your answer is confirmed.  The maximum area that can be obtained is indeed 2*sqrt(3) - 3 ~= 0.46410161513775439.

Posted by Dej Mar on 2007-09-30 22:48:00