1. **State the problem:** We have a right isosceles triangle with angles 45°, 45°, and 90°, and the hypotenuse length is 22. We need to find the length of each leg. 2. **Formula and rules:** In a 45°-45°-90° triangle, the legs are equal in length, and the hypotenuse is $\sqrt{2}$ times the length of each leg. This relationship can be written as: $$\text{hypotenuse} = \text{leg} \times \sqrt{2}$$ 3. **Set up the equation:** Let the length of each leg be $x$. Then: $$22 = x \times \sqrt{2}$$ 4. **Solve for $x$:** $$x = \frac{22}{\sqrt{2}}$$ 5. **Rationalize the denominator:** $$x = \frac{22}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{22 \sqrt{2}}{2}$$ 6. **Simplify the fraction:** $$x = 11 \sqrt{2}$$ 7. **Conclusion:** Each leg of the triangle has length $11 \sqrt{2}$. **Final answer:** C. $11\sqrt{2}$