1. **State the problem:** We have a right triangle with hypotenuse 13, one leg 7, and the other leg $x$. We need to find $x$ rounded to the nearest hundredth. 2. **Formula used:** In a right triangle, the Pythagorean theorem applies: $$x^2 + 7^2 = 13^2$$ This means the sum of the squares of the legs equals the square of the hypotenuse. 3. **Calculate squares:** $$x^2 + 49 = 169$$ 4. **Isolate $x^2$:** $$x^2 = 169 - 49$$ $$x^2 = 120$$ 5. **Find $x$ by taking the square root:** $$x = \sqrt{120}$$ 6. **Simplify and approximate:** $$x \approx 10.954$$ 7. **Round to nearest hundredth:** $$x \approx 10.95$$ **Final answer:** The length of side $x$ is approximately **10.95**.