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Solution to puzzle 14: Two ladders in an alley

Consider the following sequence of diagrams.  In each, like-colored triangles are similar.  This follows because the alley walls are parallel.

Two sloping, but parallel, ladders; similar triangles highlighted.

By similar triangles, 9/h = h/4.
Hence h2 = 36.

Rejecting the negative root, h, the vertical height of the intersection above the ground, is 6 feet.


Further reading

  1. Crossed Ladders Theorem

Source: Original, with thanks to S. Owen on wu :: forums for suggesting the extension from vertical to (parallel) sloping alley walls

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