1. **State the problem:** We have a right triangle with legs of lengths 21 and 16, and we need to find the length of the hypotenuse $x$. 2. **Formula used:** In 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:** Substitute $a=21$ and $b=16$: $$x^2 = 21^2 + 16^2$$ 4. **Calculate squares:** $$21^2 = 441$$ $$16^2 = 256$$ 5. **Sum the squares:** $$x^2 = 441 + 256 = 697$$ 6. **Find $x$ by taking the square root:** $$x = \sqrt{697}$$ 7. **Calculate the square root and round to the nearest tenth:** $$x \approx 26.4$$ **Final answer:** The length of the hypotenuse $x$ is approximately **26.4**.