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: solution by Penny)

Penny, draw a 3-inch square on a paper, and extend the bottom to the right to represent the floor. Extend the left side upward to represent the wall. Then get a 12-inch ruler. See that if you make the ruler be at a 45-degree angle, touching the wall and the floor at the ends of one of its edges, that it will not touch the 3-inch square at all. You have to bring the base in, while raising the end on the wall, so as to allow the ruler just to touch the top right vertex of the box.

(or you could bring the top down while the bottom goes right, but that would not maximize the height.)

And Penny, you'd better get some sleep if you are this exhausted.

Posted by Charlie on 2003-12-09 11:44:03