1. The problem is to find the length of the hypotenuse $x$ in a right-angled triangle where the other two sides are 12 and 16. 2. We use the Pythagorean Theorem which states: $$x^2 = a^2 + b^2$$ where $a$ and $b$ are the legs of the triangle. 3. Substitute the known values: $$x^2 = 12^2 + 16^2$$ 4. Calculate the squares: $$x^2 = 144 + 256$$ 5. Add the values: $$x^2 = 400$$ 6. Take the square root of both sides to solve for $x$: $$x = \sqrt{400}$$ 7. Simplify the square root: $$x = 20$$ Final answer: $x = 20$