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A ladder, 6.5 m long, rests against a vertical wall. If the foot of the ladder is 2.5 m from the foot of the wall, find up to how much height does the ladder reach?

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#### Solution

**Given :**

Length of ladder = 6.5 m

Length of the foot of the wall = 2.5 m

**To find:** Height AC According to Pythagoras Theorem,

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

(6.5)^{2} = (2.5)^{2} + (AC)^{2}42.25 = 6.25 + AC^{2}AC^{2} = 42.25 – 6.25 = 36 m

AC = `sqrt(6xx6)` = 6 m

∴ Height of wall = 6 m

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