Planks across a ditch part 1
Consider an L-shaped ditch with straight sides and both legs of the same uniform width.
How wide can a ditch be bridged with two 10 foot planks?
Note: consider the planks to be rigid line segments - very thin yet strong. They can only be laid across each other or either side of the ditch.
The answer is 10.6066017178.
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1 solution
Lay the first plank from A to B at a 45-degree angle. From A to the outer corner is 2 1 0 feet.
Lay the second plank from the midpoint of the first to the inner corner. The greatest distance from outer to inner corner is 2 1 5 ≈ 1 0 . 6 0 6 6 0 1 7 1 7 8 feet