1. **State the problem:** We have a right-angled triangle with two sides given: one side is 7 cm and the other is 5 cm. We need to find the length of the hypotenuse. 2. **Formula used:** In a right-angled triangle, the Pythagorean theorem applies: $$c^2 = a^2 + b^2$$ where $c$ is the hypotenuse, and $a$ and $b$ are the other two sides. 3. **Apply the formula:** Substitute $a = 7$ cm and $b = 5$ cm: $$c^2 = 7^2 + 5^2$$ $$c^2 = 49 + 25$$ $$c^2 = 74$$ 4. **Find $c$ by taking the square root:** $$c = \sqrt{74}$$ 5. **Simplify the square root if possible:** 74 is not a perfect square and cannot be simplified further. 6. **Calculate the approximate value:** $$c \approx 8.6 \text{ cm}$$ **Final answer:** The hypotenuse is approximately 8.6 cm.