Question

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?

Answer 1

Let, length of ladder be AD = BE = `l` m

In ΔACD, by Pythagoras theorem

AD² = AC² + CD²

⇒ `l`² = 8² + 6²              .....(i)

In ΔBCE, by pythagoras theorem

BE2 = BC² + CE²

⇒ `l`² = BC² + 8²             .......(ii)

Compare (i) and (ii)

BC² + 8² = 8² + 6²

⇒ BC² = 6²

⇒ BC = 6m