1. **State the problem:** We have a right triangle with base $12$ cm, height $16$ cm, and hypotenuse $c$. We need to find the perimeter, which is the sum of all sides. 2. **Formula used:** The hypotenuse $c$ can be found using the Pythagorean theorem: $$c = \sqrt{a^2 + b^2}$$ where $a$ and $b$ are the legs of the right triangle. 3. **Calculate the hypotenuse:** $$c = \sqrt{12^2 + 16^2} = \sqrt{144 + 256} = \sqrt{400} = 20$$ 4. **Calculate the perimeter:** $$P = a + b + c = 12 + 16 + 20 = 48$$ 5. **Answer:** The perimeter of the triangle is $48$ centimeters.