Question

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

Answer 1

Answer:

width=17cm

Step-by-step explanation:

ladder height =13cm

window height =12cm

therefore 13 square -12 square

=5cm

ladder placedto the other end

so the height of the ladder does not change

therefore =13 square- 5 square

=12

therefore width of street=12+5

=17cm

Answer 2

★ Given:-

A ladder 13 m long reaches a window which is 12 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 5 m high.

★ To Find:-

The width of the street.

★ Solution:-

Let PQ be the street and R be the foot of the ladder.

Let S and T be the windows at the heights of 5 m and 12 m respectively from the ground.

Then, RS and RT are two positions of the ladder.

Clearly, PS = 5 m, QT = 12 m, RT = RS = 13 m

From right ΔSPR, we have

PR² + PS² = RS²

⇒ PR² = RS² - PS²

⇒ PR² = (13² - 5²)

⇒ PR² = (169 - 25)

⇒ PR² = 144

⇒ PR² = (12)²

⇒ PR² = 12

From right ΔRQT,

RQ² + QT² = RT²

⇒ RQ² = RT² - QT²

⇒ RQ² = (13² - 12²)

⇒ RQ² = (169 - 144)

⇒ RQ² = 25²

⇒ RQ² = (5)²

⇒ RQ² = 5

Hence, the width of the street = PQ = PR + RQ = (12 - 5) m = 17 m. ✔