Question

a ladder 15m long reaches a window which is 9m 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 Windows 12 m high .find the width of the street ​

Answer 1

Answer: 21 mts

Step-by-step explanation: See the photo attached.

Answer 2

Solution :

Let AB be the street and C be the food of the ladder. Let D and E be the given windows such that AD = 9 m and BE = 12 m.

Then, CD and CE are the two positions of the ladder.

Clearly, ∠CAD = 90°, ∠CBE = 90° and CD = CE = 15 m.

$\:$

From right ∆CAD, we have

CD² = AC² + AD² [by Pythagoras' theorem]

➡ AC² = CD² - AD²

➡ AC² = [(15)² - (9)²] m²

➡ AC² = (225 - 81) m²

➡ AC² = 144 m²

➡ AC² = √144 m

➡ AC² = 12 m

$\:$

From right ∆CBE, we have

CE² = CB² + BE² [by Pythagoras' theorem]

➡ CB² = CE² - BE²

➡ CB² = [(15)² - (12)²] m²

➡ CB² = (225 - 144) m²

➡ CB² = 81 m²

➡ CB = √81 m

➡ CB = 9 m

$\:$

Width of the street = AC + CB = 12m + 9m = 21 m.

___________________________

Answer :

The width of the street = 21 m.