1. **State the problem:** We need to find the value of $x$, the hypotenuse of a right triangle with legs 10 and 12. 2. **Formula used:** For a right triangle, the Pythagorean theorem applies: $$x^2 = a^2 + b^2$$ where $a$ and $b$ are the legs, and $x$ is the hypotenuse. 3. **Apply the formula:** Here, $a=10$ and $b=12$, so: $$x^2 = 10^2 + 12^2$$ 4. **Calculate squares:** $$x^2 = 100 + 144 = 244$$ 5. **Find $x$ by taking the square root:** $$x = \sqrt{244}$$ 6. **Simplify and approximate:** $$x \approx 15.6204993518$$ 7. **Round to the nearest tenth:** $$x \approx 15.6$$ **Final answer:** $x = 15.6$