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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.
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Solution
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.
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