A right triangle has legs of length 9 and 12. What is the length of the hypotenuse?

Use the Pythagorean theorem with legs 9 and 12: $c^2 = 9^2 + 12^2 = 81 + 144 = 225$, so $c = \sqrt{225} = 15$. This is a 3-4-5 triangle scaled by 3, which is a quick way to confirm the answer: $3 \cdot 3 = 9$, $3 \cdot 4 = 12$, and $3 \cdot 5 = 15$. The most common wrong answer is 21, which comes from adding the legs instead of squaring them. Another is $\sqrt{63} \approx 7.9$, from subtracting $144 - 81$, which would be the answer only if 12 were the hypotenuse. The hypotenuse is always the longest side.