To find the length of the hypotenuse in a right triangle with side lengths 9 and 12, you can use the Pythagorean theorem, which states:
\[ c = \sqrt{a^2 + b^2} \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides.
Plugging in the values:
\[ c = \sqrt{9^2 + 12^2} \] \[ c = \sqrt{81 + 144} \] \[ c = \sqrt{225} \] \[ c = 15 \]
Thus, the length of the hypotenuse is 15.