To find the length of the hypotenuse of a right triangle when the lengths of the two legs are known, we can use the Pythagorean theorem. The theorem states:
\[ c^2 = a^2 + b^2 \]
where:
- \( c \) is the length of the hypotenuse,
- \( a \) and \( b \) are the lengths of the two legs.
In this case, let \( a = 12 \) cm and \( b = 9 \) cm. Plugging in the values:
\[ c^2 = 12^2 + 9^2 \]
Calculating \( 12^2 \) and \( 9^2 \):
\[ 12^2 = 144 \] \[ 9^2 = 81 \]
Now, we can add these two results:
\[ c^2 = 144 + 81 = 225 \]
Now, we take the square root of both sides to find \( c \):
\[ c = \sqrt{225} = 15 \text{ cm} \]
Thus, the measure of the hypotenuse is \( 15 \) cm. Since no rounding is necessary, the final answer is:
\[ \boxed{15} \] cm.