A right triangle has legs of length 5 and 12. What is the length of the hypotenuse?

Apply the Pythagorean theorem: $c^2 = 5^2 + 12^2 = 25 + 144 = 169$, so $c = \sqrt{169} = 13$. This is a well-known Pythagorean triple (5, 12, 13), so you can recognize it without any calculation. A common wrong answer is 17, which comes from adding the legs instead of squaring and summing. Another is $\sqrt{119} \approx 10.9$, which comes from subtracting $144 - 25$, as if 12 were the hypotenuse. A third is 7, the difference of the legs. The hypotenuse is the longest side and must exceed both legs.