1. **State the problem:** We have a 45°-45°-90° right triangle with one leg labeled $c$ and the other leg labeled $3\sqrt{2}$ cm. We need to find $c$ in simplest radical form. 2. **Recall the properties of a 45°-45°-90° triangle:** In such a triangle, the legs are congruent, and the hypotenuse is $\sqrt{2}$ times the length of each leg. 3. **Identify the sides:** Since the triangle is 45°-45°-90°, the two legs are equal, and the hypotenuse is opposite the right angle. 4. **Given:** The side labeled $3\sqrt{2}$ cm is the hypotenuse. 5. **Use the formula for the hypotenuse:** $$\text{hypotenuse} = \text{leg} \times \sqrt{2}$$ 6. **Set up the equation:** $$3\sqrt{2} = c \times \sqrt{2}$$ 7. **Divide both sides by $\sqrt{2}$ to solve for $c$:** $$c = \frac{3\sqrt{2}}{\sqrt{2}}$$ 8. **Cancel $\sqrt{2}$:** $$c = 3\cancel{\sqrt{2}} / \cancel{\sqrt{2}} = 3$$ 9. **Final answer:** $$c = 3$$ So, the length of side $c$ is 3 centimeters.