Question

Walls of two buildings on either side of a street are parallel to each other. A ladder 5.8 m long is placed on the street such that its top just reaches the window of a building at the height of 4 m. On turning the ladder over to the other side of the street, its top touches the window of the other building at a height 4.2 m. Find the width of the street.

Answer 1

Let AC and CE represent the ladder of length 5.8 m, and A and E represent windows of the buildings on the opposite sides of the street. BD is the width of the street.

AB = 4 m and ED = 4.2 m

In ∆ABC, ∠B = 90° [Given]

AC² = AB² + BC² [Pythagoras theorem]

∴ CD = 4m (ii) [Taking square root of both sides]

Now, BD = BC + CD [B – C – D]

= 4.2 + 4 [From (i) and (ii)] 

= 8.2 m 

∴ The width of the street is 8.2 metres.