A ladder 13 m long reaches a window which is 12 m above the ground on side of a street Keeping its f......

A ladder 13 m long reaches a window which is 12 m above the ground on side of a street. Keeping its foot at the same point, the ladder is turned to the other side of the street to each a window 5m high, then the width of the street is :

Length of the ladder = AC = CE = 13 m
Height wall the ladder touches = AB = 12 m
Join A and E to C is a foot of the ladder,
Angle ABC = 90
i) in triangle ABC
BC^2 = AC^2 - AB^2 [ since Pythagoras theorem ]
= ( 13 )^2 - ( 12 )^2
= 169 - 144
= 25
Therefore ,
BC = 5 m --------( 1 )
ii ) If ladder turned to other side of the street
keeping its foot at the same point ' C '
ED = 5m,
CE = length of the ladder = 13 m
From triangle CDE , angle CDE = 90
CD^2 = CE^2 - DE^2 [ By Pythagoras theorem ]
= ( 13 )^2 - 5^2
= 169 - 25
= 144
Therefore,
CD = 12 m--------( 2 )
Now ,
Width of the street = BC + CD
= 5 m+ 12 m [ from ( 1 ) and ( 2 ) ]
= 17 m

By: Amit Kumar