1. **State the problem:** We have a right triangle with legs measuring 5.4 cm and 12.8 cm, and we need to find the length of the hypotenuse $x$ cm. 2. **Formula used:** In a right triangle, the Pythagorean theorem applies: $$x^2 = a^2 + b^2$$ where $a$ and $b$ are the legs, and $x$ is the hypotenuse. 3. **Apply the formula:** Substitute $a = 5.4$ and $b = 12.8$: $$x^2 = 5.4^2 + 12.8^2$$ 4. **Calculate squares:** $$5.4^2 = 29.16$$ $$12.8^2 = 163.84$$ 5. **Sum the squares:** $$x^2 = 29.16 + 163.84 = 193$$ 6. **Find $x$ by taking the square root:** $$x = \sqrt{193}$$ 7. **Calculate the square root:** $$x \approx 13.89$$ **Final answer:** $$x \approx 13.89 \text{ cm}$$