1. The problem asks to find the value of $x$ in the first figure, which is a right triangle with legs 12 cm and 16 cm, and hypotenuse $x$ cm. 2. We use the Pythagorean theorem for right triangles: $$x^2 = a^2 + b^2$$ where $a$ and $b$ are the legs. 3. Substitute the given values: $$x^2 = 12^2 + 16^2$$ 4. Calculate the squares: $$x^2 = 144 + 256$$ 5. Sum the values: $$x^2 = 400$$ 6. Take the square root of both sides: $$x = \sqrt{400}$$ 7. Simplify the square root: $$x = 20$$ Therefore, the value of $x$ is 20 cm.