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Question
The foot of a ladder is 6m away from a wall and its top reaches a window 8m above the ground. If the ladder is shifted in such a way that its foot is 8m away from the wall to what height does its tip reach?
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Solution
Let AC be the ladder and A be the position of the window which is 8m above the ground.
Now, the ladder is shifted such that its foot is at point D which is 8m away from the wall.
∴ BD = 8m
At this instance, the position of the ladder is DE.
∴ AC = DE
Using Pythagoras theorem in ΔABC,
AC2 = AB2 + BC2
= (8m)2 + (6m)2
= 64m2 + 36m2
= 100m2
= (10m)2
∴ AC = DE = 10m
Using Pythagoras theorem in ΔDBE,
BE2 = DE2 - BD2
⇒ BE2 = (10m)2 - (8m)2
= 100m2 - 64m2
= 36m2
= (6m)2
⇒ BE = 6m
Thus, the required height up to which the ladder reaches is 6m above the ground.
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