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Question
The top of a ladder of length 15 m reaches a window 9 m above the ground. What is the distance between the base of the wall and that of the ladder?
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Solution
Let LN be the ladder of length 15 m that is resting against a wall. Let M be the base of the wall and L be the position of the window.
The window is 9 m above the ground. Now, MN is the distance between the base of the wall and that of the ladder.
In the right-angled triangle LMN, ∠M = 90°. Hence, side LN is the hypotenuse.
According to Pythagoras' theorem,
l(LN)2 = l(MN)2 + l(LM)2
⇒ (15)2 = l(MN)2 + (9)2
⇒ 225 = l(MN)2 + 81
⇒ l(MN)2 = 225 − 81
⇒ l(MN)2 = 144
⇒ l(MN)2 = (12)2
⇒ l(MN) = 12
∴ Length of seg MN = 12 m.
Hence, the distance between the base of the wall and that of the ladder is 12 m.
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