Question 48

A ladder 15 m long reaches a window which is 9 m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 12 m high. Find the width of the street.

Solution

As per the given question,

Using pythagoras theorem,

$$BC^{2} = AC^{2} - AB^{2}$$

$$BC^{2} = 15^{2} - 12^{2} = 225 - 144 = 81$$

$$BC = 9\ m $$

$$CD^{2} = EC^{2} - ED^{2}$$

$$CD^{2} = 15^{2} - 9^{2} = 225 - 81 = 144$$

$$CD = 12\ m $$

Width of the street = $$12 + 9 = 21\ m$$

Hence, option B is the correct answer.

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