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Leaning Ladders

Problem

Two ladders, both 4 metres in length, are leaned up against opposite walls in a corridor, 3 metres wide, as shown in the diagram.

How far above the ground do the two ladders cross?


Solution

By symmetry the intersection point is half the height the ladders reach up the opposite wall.

Using the Pythagorean Theorem, 42 = $b$2 + 32 implies $b$ = radical7

So, $a$ = radical7/2 approximately 1.32 metres.

What if the two ladders are different lengths? Try 4 metres and 5 metres.

Problem ID: 113 (Apr 2003)     Difficulty: 2 Star

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