1. **State the problem:** We need to find the length of the hypotenuse of an isosceles right triangle where each leg measures 12 cm. 2. **Recall the formula:** In an isosceles right triangle, the legs are equal, and the hypotenuse $h$ is given by the Pythagorean theorem: $$h = \sqrt{leg^2 + leg^2}$$ 3. **Apply the formula:** Substitute the leg length 12 cm: $$h = \sqrt{12^2 + 12^2}$$ 4. **Calculate inside the square root:** $$h = \sqrt{144 + 144}$$ $$h = \sqrt{288}$$ 5. **Simplify the radical:** Factor 288 as $144 \times 2$: $$h = \sqrt{144 \times 2}$$ Use the property $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$: $$h = \sqrt{144} \times \sqrt{2}$$ Since $\sqrt{144} = 12$: $$h = 12\sqrt{2}$$ 6. **Final answer:** The length of the hypotenuse is $12\sqrt{2}$ cm.