Ha. Funnily enough my father tacked this on to an email I received from him this morning, coming on the heels of my defense of the real-world.
I enjoyed this decidedly non-real-world problem and thought you might too.
Consider a unit square that encloses a unit equilateral triangle:
As shown, the area of the square is 1, and the area of the triangle is sqrt(3)/2. What is the largest equilateral triangle that can be inscribed in the square?
Happy problem solving, everyone!