1. **State the problem:** We have a right triangle with one leg measuring 12 cm, the hypotenuse measuring 39 cm, and the other leg labeled as $x$ cm. We need to find the length of $x$. 2. **Formula used:** In a right triangle, the Pythagorean theorem applies: $$a^2 + b^2 = c^2$$ where $a$ and $b$ are the legs and $c$ is the hypotenuse. 3. **Apply the formula:** Let the legs be 12 cm and $x$ cm, and the hypotenuse be 39 cm. $$12^2 + x^2 = 39^2$$ 4. **Calculate squares:** $$144 + x^2 = 1521$$ 5. **Isolate $x^2$:** $$x^2 = 1521 - 144$$ $$x^2 = 1377$$ 6. **Find $x$ by taking the square root:** $$x = \sqrt{1377}$$ 7. **Calculate the square root:** $$x \approx 37.1$$ 8. **Conclusion:** The length $x$ is approximately 37.1 cm, which corresponds to option A.