To find the length of the hypotenuse of a right triangle with sides of length 12 and 16, you can use the Pythagorean theorem, which states:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides.
Plugging in the values:
\[ c^2 = 12^2 + 16^2 \] \[ c^2 = 144 + 256 \] \[ c^2 = 400 \]
Now, take the square root of both sides:
\[ c = \sqrt{400} \] \[ c = 20 \]
Therefore, the length of the hypotenuse is 20.