1. **Problem statement:** We have a right triangle with hypotenuse 24 and base 9, and a vertical side labeled $x$. We need to find the length of $x$. 2. **Formula used:** In a right triangle, the Pythagorean theorem states: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse, and $a$, $b$ are the legs. 3. **Apply the formula:** Here, the hypotenuse $c = 24$, the base $a = 9$, and the vertical side $b = x$. So, $$9^2 + x^2 = 24^2$$ 4. **Calculate squares:** $$81 + x^2 = 576$$ 5. **Isolate $x^2$:** $$x^2 = 576 - 81$$ $$x^2 = 495$$ 6. **Find $x$ by taking the square root:** $$x = \sqrt{495}$$ 7. **Simplify the square root:** $$495 = 9 \times 55$$ $$x = \sqrt{9 \times 55} = \sqrt{9} \times \sqrt{55} = 3\sqrt{55}$$ 8. **Approximate the value:** $$x \approx 3 \times 7.416 = 22.248$$ 9. **Final answer:** $$x \approx 22.24$$ So, the correct choice is D. 22.24.