Question

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

Answer 1

Your query -

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

Answer -

• Let AB be the width of the street and let C and D be windows at heights of 5 m and 12 m respectively from the ground .

• Let E be the foot of the ladder .

• Then EC and ED are the two positions of the ladder .

Clearly , AC = 5m , BD = 12 m , EC = ED = 13 m , and Angle CAE = Angle DBE = 90°

In right triangle CAE , we have

→ CE² = AC² + AE² [ by Pythagoras theorem ]

→ ( 13m )² = ( 5m )² + AE²

→ AE² = ( 13m )² - ( 5m )²

→ AE² = ( 169 - 25 )m²

→ AE² = 144 m²

→ AE = 12m $\pink{\bigstar}$

In right triangle DBE , we have

→ DE² = BD² + EB²

→ (13 m)² = (12 m)² + EB²

→ EB² = (13 m)² – (12 m)²

→ EB² = (169 – 144) m²

→ EB² = 25 m²

→ EB = 5 m $\blue{\bigstar}$

Adding (1) and (2), we get

AE + EB = (12 +5) m

→ AB = 17 m

hence , the width of the street is 17 m $\orange{\bigstar}$

Answer 2

Answer:

Your question-----

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

Answer -

• Let AB be the width of the street and let C and D be windows at heights of 5 m and 12 m respectively from the ground .

• Let E be the foot of the ladder .

• Then EC and ED are the two positions of the ladder .

Clearly , AC = 5m , BD = 12 m , EC = ED = 13 m , and Angle CAE = Angle DBE = 90°

In right triangle CAE , we have

→ CE² = AC² + AE² [ by Pythagoras theorem ]

→ ( 13m )² = ( 5m )² + AE²

→ AE² = ( 13m )² - ( 5m )²

→ AE² = ( 169 - 25 )m²

→ AE² = 144 m²

→ AE = 12m \pink{\bigstar}★

In right triangle DBE , we have

→ DE² = BD² + EB²

→ (13 m)² = (12 m)² + EB²

→ EB² = (13 m)² – (12 m)²

→ EB² = (169 – 144) m²

→ EB² = 25 m²

→ EB = 5 m \blue{\bigstar}★

Adding (1) and (2), we get

AE + EB = (12 +5) m

→ AB = 17 m

hence , the width of the street is 17 m ★