1. **State the problem:** We have a right triangle ABC with a right angle at C, angle $\angle A = 45^\circ$, and hypotenuse $AB = 12$. We need to find the length of side $BC$. 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 $\angle A = 45^\circ$ and $\angle C = 90^\circ$, the remaining angle $\angle B$ is also $45^\circ$. Therefore, triangle ABC is an isosceles right triangle with legs $AC$ and $BC$ equal. 4. **Use the formula for the hypotenuse:** $$AB = \text{leg} \times \sqrt{2}$$ Let the leg length be $x = BC$. 5. **Set up the equation:** $$12 = x \times \sqrt{2}$$ 6. **Solve for $x$:** $$x = \frac{12}{\sqrt{2}}$$ 7. **Rationalize the denominator:** $$x = \frac{12}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{12\sqrt{2}}{2}$$ 8. **Simplify:** $$x = 6\sqrt{2}$$ **Final answer:** The length of side $BC$ is $6\sqrt{2}$.