## 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, 4^{2} = `b`^{2} + 3^{2} `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