A ladder 40 m40 m long reaches a window which is 24 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 m high. Find the width of the street.

A 24 m 32 m C B E D 40 m 40 m


Answer:

56 m56 m

Step by Step Explanation:
  1. Let ABAB be the street and let CC be the foot of the ladder. Let DD and EE be the given windows such that AD=24 mAD=24 m and BE=32 mBE=32 m.

    Then, CDCD and CECE are the two positions of the ladder.

    Clearly, CAD=90CAD=90, CBE=90CBE=90 and CD=CE=40 m.CD=CE=40 m.

    From right ΔCADΔCAD, we have [Math Processing Error]
  2. From right ΔCBE , we have [Math Processing Error]
  3. Therefore, width of the street = AC+CB = 32 m+24 m=56 m.

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