Foot of a 10 m long ladder leaning against a vertical well is 6 m away from the base of the wall. Find the height of the point on the wall where the top of the ladder reaches.

Given,

Let PQ be a vertical wall and PR = 10m is a ladder.


The top of the ladder reaches to P and distance of ladder from the base of the wall QR is 6m.



In right angled ∆PQR,


PR2 = PQ2 + QR2 [by Pythagoras theorem]


⇒ (10)2 = PQ2 + (6)2


⇒ 100 = PQ2 + 36


⇒ PQ2 = 100 – 36 = 64


∴ PQ = √64 = 8 cm


Hence, the height of the point on the wall where the top of the ladder reaches is 8cm.


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