A ladder 15 m long reaches a window which is 9 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 12 m high. Find the width of the street.
Pythagoras Theorem
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Question

A ladder 15 m long reaches a window which is 9 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 12 m high. Find the width of the street.

Pythagoras Theorem

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KnowledgeBoat · Accepted Answer

From figure, Let width of the street be AB = AC + BC Let CD and CE be the ladder at different positions. By Pythagoras theorem, Hypotenuse2 = Perpendicular2 + Base2 In triangle ADC, ⇒ CD2 = AD2 + AC2 ⇒ 152 = 92 + AC2 ⇒ 225 = 81 + AC2 ⇒ AC2 = 225 - 81 ⇒ AC2 = 144 ⇒ AC = ⇒ AC = 12 m In triangle BCE, ⇒ CE2 = BE2 + BC2 ⇒ 152 = 122 + BC2 ⇒ 225 = 144 + BC2 ⇒ BC2 = 225 - 144 ⇒ BC2 = 81 ⇒ BC = ⇒ BC = 9 m AB = AC + BC = 12 + 9 = 21 m. Hence, the width of the street is 21 m.

Mathematics

A ladder 15 m long reaches a window which is 9 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 12 m high. Find the width of the street.

Pythagoras Theorem

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