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.