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A 6.5 m long ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall. Find the height of the wall where the top of the ladder touches it.

Answer:

Given, a ladder 6.5 m long is placed against a wall such that its foot is 2.5 m away from wall.

Let AC be the wall and AB be the ladder,

BC is the distance of foot of the ladder from the wall

So, AB = 6.5 cm and BC = 2.5 m

Therefore, by Pythagoras theorem,

AB^{2} = AC^{2} + BC^{2}

6.5^{2} = AC^{2} + 2.5^{2}

AC^{2 }= 42.25 – 6.25

AC^{2 }= 36

AC = 6m

∴ Height of wall where the top of ladder touches = 6 m

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