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# A painter sets a ladder up to reach the bottom of a second storey window 16 feet above the ground. The base of the ladder is 12 feet from the house. While the painter mixes the paint a neighbour’s dog bumps the ladder which moves the base 2 feet farther away from the house. How far up side of the house does the ladder reach?

Answer :

__We know that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.__

Consider ΔABC,

⇒ BC^{2} = AB^{2} + AC^{2}

⇒ BC^{2} = 16^{2} + 12^{2}

⇒ BC^{2} = 256 + 144

⇒ BC^{2} = 400

∴ BC = √400 = 20 cm (Length of ladder)

Now after the ladder being pushed 2 feet farther, consider ΔBDE,

⇒ DE^{2} = BD^{2} + BE^{2}

⇒ 20^{2} = 14^{2} + BE^{2}

⇒ BE^{2} = 400 – 196 = 204

⇒ BE = √204 = = 2√51 cm

∴ The ladder reaches 2√51 cm far up side the house.

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