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 solution by SilverKnight)

So long as we eventually use Excel anyway, we might as well make it easy:
Let cell A2 start at 4, representing x.
in B2: =3*A2/(A2-3) representing y, based on the similarity of the bottom little triangle to the large triangle.
in C2: =A2^2+B2^2
Then set solver to making C2 be 144 by changing A2. You still get 4.086599979
(well, there's rounding at the end...)

Posted by Charlie on 2003-12-09 11:48:29