Question

Walls of two buildings on either side of a street are parellel to each other
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

Answer:

The width of the street is 8.2 m.

Step-by-step-explanation:

NOTE: Refer to the attachment for the diagram.

The walls are assumed to be perpendicular to the street.

In figure,

Seg XB & Seg YD represents walls of two buildings.

Seg BD represents the street.

Seg AC represents the initial position of ladder.

Seg CE represents final position of ladder.

We have given that,

AC = CE = 5.8 m,

AB = 4 m

DE = 4.2 m

Now,

In △ABC, ∠ABC = 90°

∴ AC² = AB² + BC² - - [ Pythagors theorem ]

⇒ ( 5.8 )² = 4² + BC²

⇒ 33.64 = 16 + BC²

⇒ BC² = 33.64 - 16

⇒ BC² = 17.64

⇒ BC = 4.2 m - - [ Taking square roots ]

Now,

In △EDC, ∠EDC = 90°

∴ CE² = DE² + CD² - - [ Pythagors theorem ]

⇒ ( 5.8 )² = ( 4.2 )² + CD²

⇒ 33.64 = 17.64 + CD²

⇒ CD² = 33.64 - 17.64

⇒ CD² = 16

⇒ CD = 4 m - - [ Taking square roots ]

Now,

BD = BC + CD - - [ B - C - D ]

⇒ BD = 4.2 + 4

⇒ BD = 8.2 m

∴ The width of the street is 8.2 m.