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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 window 12m high. Find the width of the street.
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Solution
let O be the foot of the ladder. Let AO be the position of the ladder when it touches the window at A which is 9m high and CO be the position of the ladder when it touches the window at C which is 12m high.
Using Pythagoras theorem,
In ΔAOB,
BO2 = AO2 - AB2
BO2 = (15m)2 - (9m)2
BO2 = 225m2 - 81m2
BO2 = 144m2
BO2 = (12m)2
BO2 = 12m
Using Pythagoras theorem in ΔCOB,
DO2 = CO2 - CD2
DO2 = (15m)2 - (12m)2
DO2 = 225m2 - 144m2
DO2 = 81m2
DO = 9m
Width of the street
= DO + BO
= 9m + 12m
= 21m.
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