Question

A ladder 13m long reaches a window which is 12m 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 5m high. Find the width of the street

Answer 1

Hi ,

Draw a rough diagram with data given

in the problem.
A
I
l12
| |E
l | 5
l |
l_________|__________________|D
B C

Let us assume ,

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

I hope this helps you.

******

Answer 2

Answer:

Let us assume ,

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

I hope this helps you.