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 the length of the ladder be 5.8 m.

According to Pythagoras theorem,

In ΔEAB,

EA² + AB² = EB²

∴ (4.2)² + AB² = (5.8)²

∴ 17.64 + AB² = 33.64

∴ AB² = 33.64 − 17.64

∴ AB² = 16

∴ AB = 4 m

In ∆DCB,

DC² + CB² = DB²

∴ (4)² + CB² = (5.8)²

∴ 16 + CB² = 33.64

∴ CB² = 33.64 − 16

∴ CB² = 17.64

∴ CB = 4.2 m

From (1) and (2), we get

AB + BC = 4 + 4.2 = 8.2 m

∴ the width of the street is 8.2 m.