1. **State the problem:** We are given a right-angled triangle with two shorter sides (legs) measuring 14 cm and 26 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 legs. 3. **Substitute the values:** $$c^2 = 14^2 + 26^2$$ 4. **Calculate the squares:** $$c^2 = 196 + 676$$ 5. **Add the squares:** $$c^2 = 872$$ 6. **Find the hypotenuse by taking the square root:** $$c = \sqrt{872}$$ 7. **Calculate the square root:** $$c \approx 29.5307$$ 8. **Round to 1 decimal place:** $$c \approx 29.5$$ **Final answer:** The length of the hypotenuse is approximately 29.5 cm.