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 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 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 = 16 m.
Hence, the distance between base of the wall and that of the ladder is 12 m.

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