Question 26

In an alley a $$25\text{ m}$$ tall ladder is placed against a wall touching the wall at a point $$24\text{ m}$$ high from the level ground. When the ladder is switched over to the wall on the other side of the alley, without changing the base position of the ladder, it touches the wall at a point $$7\text{ m}$$ high from the ground. The width of the alley is

Solution

The foot of the ladder is $$\sqrt{25^2 - 24^2} = \sqrt{49} = 7\text{ m}$$ from the first wall and $$\sqrt{25^2 - 7^2} = \sqrt{576} = 24\text{ m}$$ from the other wall. So the width of the alley is $$7 + 24 = 31\text{ m}$$.

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