Suppose you're trying to bridge a moat (and thus avoid the alligators!) with 10 foot long wooden planks. You might think that a 10 foot moat would be the widest moat you could safely cross. But, if the moat is a bit wider than 10 feet but has a square corner, and if you have more than one 10 foot long plank, you might want to try placing two of the planks as shown in the diagram at right.

Click to enlarge

This will, in fact, allow you to safely bridge a moat wider than 10 feet. The question for this week is this: how wide can the moat be for this scheme to work? As usual, we want an exact answer (which should include some square roots).