Question

a lader 17m lo reavh a Windows whichever is 8m above grounds, on one side of the street .keeping its fot at samw point, the lader is turned to the othr side of the street to reach a window at a height 15m . fond the widhth of the street. ​

Answer 1

★Correct question:-

• A ladder 17 m long reaches a window which is 8 m above the ground, on one side of the street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window at a height of 15 m. Find the width of the street.

Given:-

• Length of the ladder when it reaches a window ⟶ 17 m which 8 m above the ground.

• Height of the ladder when reached a window to other side of the street ⟶ 15 m.

To find:-

• Width of the street.

Solution:-

◕ Let AB be the street and C be the foot of the ladder. Let D and E be the windows at the height of 8 m and 15 m respectively from the ground.

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

★From right ΔDAC, we have :-

➵ AC² + AD² = CD²

➵ AC² = (CD² - AD²)

➵ {(17)² - (8)²} m² = (17 + 8) (17 - 8) m² = (25 × 9) m² = 225 m²

➵ AC = √225 m = √15 × 15m = 15m

★ From right ΔCBE, we have :-

➵ CB² + BE² = CE²

➵ CB² = (CE² - BE²)

➵ {(17)² - (15)²} m² = (17 + 15) (17 - 15)m² = (32 × 2)m² = 64 m²

➵ CB = √64 m = √8 × 8m = 8m.

✰Hence, the width of the street = AB = (AC + CB) = (15 + 8)m = 23m.

$\boxed{\rm{\red{Width \ of \ Street \longrightarrow 23m }}}$

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