(Q6) A ladder 15 m long reaches a window which is 9 m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to other side of the street to reach a window 12 m high. Find the width of the street.

ABCDE9 m15 m15 m12 mxy

Solution :

Let A and D be the windows on the either sides of the street.

AC2 = AB2 + BC2

( )2 = ( )2 + BC2

BC2 = -

BC = √( ) = ( ) .....(1)

Also, CD2 = DE2 + CE2

( )2 = ( )2 + CE2

CE2 = -

CE = √( ) = ( )

∴ BE = BC + CE = + =

Width of the street = m.