#### 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 $b$ = 7

So, $a$ = 7/2 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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