To find the length of the hypotenuse of a right triangle with sides of lengths 12 and 16, we 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.
In this case, we can let \( a = 12 \) and \( b = 16 \):
\[ c^2 = 12^2 + 16^2 \] \[ c^2 = 144 + 256 \] \[ c^2 = 400 \]
Now, take the square root of both sides to find \( c \):
\[ c = \sqrt{400} = 20 \]
Thus, the length of the hypotenuse is 20.