A ladder 40 m40 m40 m long reaches a window which is 24 m24 m24 m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 32 m32 m32 m high. Find the width of the street.
Answer:
56 m56 m56 m
- Let ABABAB be the street and let CCC be the foot of the ladder. Let DDD and EEE be the given windows such that AD=24 mAD=24 mAD=24 m and BE=32 mBE=32 mBE=32 m.
Then, CDCDCD and CECECE are the two positions of the ladder.
Clearly, ∠CAD=90∘∠CAD=90∘∠CAD=90∘, ∠CBE=90∘∠CBE=90∘∠CBE=90∘ and CD=CE=40 m.CD=CE=40 m.CD=CE=40 m.
From right ΔCADΔCADΔCAD, we have [Math Processing Error] - From right ΔCBEΔCBE , we have [Math Processing Error]
- Therefore, width of the street = AC+CBAC+CB = 32 m+24 m=56 m32 m+24 m=56 m.