1. **State the problem:** We need to find the hypotenuse of a right triangle when the other two sides are 25 and 95. 2. **Formula used:** According to the Pythagorean theorem, the hypotenuse $c$ is given by: $$c = \sqrt{a^2 + b^2}$$ where $a$ and $b$ are the legs of the triangle. 3. **Substitute the values:** $$c = \sqrt{25^2 + 95^2}$$ 4. **Calculate the squares:** $$c = \sqrt{625 + 9025}$$ 5. **Add the values inside the square root:** $$c = \sqrt{9650}$$ 6. **Simplify the square root:** $$c = \sqrt{25 \times 386} = 5\sqrt{386}$$ 7. **Approximate the value:** $$c \approx 5 \times 19.6469 = 98.2345$$ **Final answer:** The hypotenuse is approximately $98.23$.