A 3' cube sits on level ground against a vertical wall. A 12' ladder on the same ground leans against the wall such that it touches the top edge of the box.

How far from the wall must the foot of the ladder be, if it is to reach maximum height whilst meeting the foregoing conditions?

(In reply to re(3): solution by Penny)

Penny, I'm sure if I went to a mind-reader she would give me change or something, but I don't understand your point. It doesn't matter what length of ladder you have, or how you set it up, there is ALWAYS a cube you could 'squeeze' in the trangle formed, so that the cube 'touches' the ladder without disturbing it. This quetion, however, gives you the cube size and ladder length and asks how you set it up.
Your answer is the specific case where the cube is precicely sqrt(L^2/8) - L being the ladder length

Posted by Lee on 2003-12-09 11:52:45