What is the area of the largest square that will fit inside a triangle
with sides 3", 4", and 5"?

(There are two ways to fit a square into a right triangle: place one
vertex of the square in the right angle of the triangle, or place one side
of the square along the hypotenuse.  Which one is larger?)

There will be a $1 prize for the best correct solution submitted by a
midshipman.

A solution is "correct" if it answers the question correctly and explains
the answer; a solution is "best" if it includes the clearest correct
explanation.  Solutions are due by noon on Thursday, October 29, 1998.
Submit solutions to Prof. Hanna at mathprob@nadn.navy.mil, or via the
mailbox in Chauvenet 301.



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Problem #77 (moving the pebbles) generated a lot of interest among math
faculty, but no midshipmen sent in solutions.  It's not too hard to find a
solution that takes 232 moves; the best known solution takes 229 moves.