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## 'Two Ladders' printed from http://nrich.maths.org/

Two ladders are propped up against facing walls as shown in the
diagram. The end of the first ladder is 10 metres above the foot of
the first wall. The end of the second ladder is 5 metres above the
foot of the second wall. At what height do the ladders cross?

Can you say other circumstances in which the ladders cross at a
height which is one third and two thirds of the heights up the
walls respectively?

Can you generalise this result for ladders at different
heights?