1. Problem: Find $x$ in a right triangle with legs 12 and 9, hypotenuse $x$. 2. Use the Pythagorean theorem: $$x^2 = 12^2 + 9^2$$ 3. Calculate squares: $$x^2 = 144 + 81 = 225$$ 4. Take the square root: $$x = \sqrt{225} = 15$$ Answer: $x = 15$