The sum of the squares of the sides of a right-angled triangle is 8,450 square units. What is the length of its hypotenuse?

Explanation

Let the sides be perpendicular p, base b, and hypotenuse h. By Pythagoras, p^2 + b^2 = h^2. The given sum is p^2 + b^2 + h^2 = 8450. Substituting p^2 + b^2 gives 2h^2 = 8450, so h^2 = 4225. Taking the square root, h = 65.

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