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

AB = 4 m and ED = 4.2 m 

In ∆ABC, ∠B = 90° [Given] 

AC² = AB² + BC² [Pythagoras theorem] 

∴ 5.8² = 4² + BC² 

∴ 5.8² – 4² = BC² 

∴ (5.8 – 4) (5.8 + 4) = BC²

∴ 1.8 × 9.8 = BC²

CE² = CD² + DE² [Pythagoras theorem] 

∴ 5.8² = CD² + 4.22 

∴ 5.8² – 4.2² = CD² 

∴ (5.8 – 4.2) (5.8 + 4.2) = CD² 

∴ 1.6 × 10 = CD² 

∴ CD² = 16 

∴ 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.