1. The problem states we have a right triangle with two side lengths given: 12 cm and 39 cm, and we need to find the length of the third side $x$. 2. We use the Pythagorean theorem for right triangles: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse (the longest side), and $a$ and $b$ are the other two sides. 3. Identify the hypotenuse: since 39 cm is longer than 12 cm, 39 cm is likely the hypotenuse. 4. Let the legs be 12 cm and $x$ cm, and the hypotenuse be 39 cm. So: $$12^2 + x^2 = 39^2$$ 5. Calculate squares: $$144 + x^2 = 1521$$ 6. Isolate $x^2$: $$x^2 = 1521 - 144$$ $$x^2 = 1377$$ 7. Take the square root of both sides: $$x = \sqrt{1377}$$ 8. Approximate the square root: $$x \approx 37.1$$ 9. Among the options, 37.1 cm is closest to $x$. Final answer: 37.1 cm (Option A)