………………… in the I-Pad factory not a creature was stirring except for... In an attempt to discover the secrets of Apple’s new i-Pad Streaming App, a team of Naim engineers decided to gain illegal entry to the i-Pad factory. Oh the shame of it!
They arrive at the factory in the dead of night and decide to try to gain entry via the roof. Naturally they aren't carrying a ladder because this would arouse suspicion among the locals. So they search for one and eventually find an old wooden ladder with a slightly rotten set of rungs. The ladder has length L. The factory roof is hard to access, even with a ladder, and on their first attempt the ladder crackles and threatens to break. They stop climbing and wonder what to do. Scouting for a way in they find a wall against which a large, cubic crate has been left, of side 1m. They reason that if they position the ladder so that it touches the ground, the wall and the outer, top edge of the crate, that this will provide sufficient support to prevent the ladder from breaking. Good.
Being exacting engineers and slaves to planning they first decide to calculate the exact distance that they must place the foot of the ladder away from the bottom edge of the crate so that it will just touch both the wall and the edge of the crate. Can they work it out before sunrise?
In terms of the ladder length L, what is the horizontal distance the foot of the ladder must be placed away from the bottom edge of the crate? Assume the ground is horizontal, the wall vertical and the crate a perfect cube.
The winner will have the most elegant formula, but you might find it more profitable to share ideas.....!