1. **State the problem:** We need to find the length of the hypotenuse $x$ in a right triangle where the legs are 6 and 10. 2. **Formula used:** According to the Pythagorean theorem, for a right triangle with legs $a$ and $b$ and hypotenuse $c$, the relationship is: $$c = \sqrt{a^2 + b^2}$$ 3. **Apply the formula:** Here, $a = 6$ and $b = 10$, so: $$x = \sqrt{6^2 + 10^2}$$ 4. **Calculate the squares:** $$6^2 = 36$$ $$10^2 = 100$$ 5. **Sum the squares:** $$36 + 100 = 136$$ 6. **Find the square root:** $$x = \sqrt{136}$$ 7. **Evaluate the square root:** $$x \approx 11.6619$$ 8. **Round to the nearest tenth:** $$x \approx 11.7$$ **Final answer:** The length of the hypotenuse $x$ is approximately **11.7**.