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The foot of a ladder is 6 m away from a wall and its top reaches a window 8 m above the ground. If the ladder is shifted in such a way that its foot is 8 m away from the wall, to what height does its tip reach?

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Let’s assume the length of ladder to be, AD = BE = x m

So, in ∆ACD, by Pythagoras theorem 

We have, 

AD2 = AC2 + CD2 

⇒ x2 = 82 + 62 … (i) 

Also, in ∆BCE, by Pythagoras theorem 

BE2 = BC2 + CE2 

⇒ x2 = BC2 + 82 … (ii) 

Compare (i) and (ii) 

BC2 + 82 = 82 + 62

⇒ BC2 + 62 

⇒ BC = 6 m 

Therefore, the tip of the ladder reaches to a height of 6 m.

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