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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?

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,

BC2 = AB2 + AC2

BC2 = 162 + 122

BC2 = 256 + 144

BC2 = 400

BC = √400 = 20 cm (Length of ladder)

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

DE2 = BD2 + BE2

202 = 142 + BE2

BE2 = 400 – 196 = 204

BE = √204 = = 2√51 cm

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

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