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

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In the figure , seg `XB` and seg `YD` represent the walls of two buildings on either side of street `BD`.
image
Seg `AC` represents the first position of the ladder and seg `CE` represents the second position of the ladder.
`AC=CE=5.8m`, `AB=4m` and `DE=4.2m`.
In `DeltaABC`, `/_ABC=90^(@)`
`:.` by Pythagoras theorem,
`AC^(2)=AB^(2)+BC^(2)`
`:.5.8^(2)=4^(2)+BC^(2)`
`:.33.64=16+BC^(2)`
`:.BC^(2)=33.64-16` `:.BC^(2)=17.64`
`:.BC=4.2m`......(Taking square roots of both the sides)
In `DeltaEDC`, `/_EDC=90^(@)`
`:.` by Pythagoras theorem,
`CE^(2)=DE^(2)+CD^(2)`
`:.5.8^(2)=4.2^(2)+CD^(2)`
`:.CD^(2)=5.8^(2)-4.2^(2)`
`:.CD^(2)=33.64-17.64` `:. CD^(2)=16`
`:.CD=4m` ......(Taking square roots of both the sides)
`BD=BC+CD`.......`(B-C-D)`
`:.BD=4.2+4`
`:.BD=8.2m`

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