1. The problem asks for the length of the hypotenuse of a right triangle with legs measuring 11 cm and 10 cm. 2. We use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse $c$ is equal to the sum of the squares of the legs $a$ and $b$: $$c^2 = a^2 + b^2$$ 3. Substitute the given leg lengths: $$c^2 = 11^2 + 10^2$$ 4. Calculate the squares: $$c^2 = 121 + 100$$ 5. Add the values: $$c^2 = 221$$ 6. To find $c$, take the square root of both sides: $$c = \sqrt{221}$$ 7. Simplify the square root if possible. Since 221 factors as $13 \times 17$, which are primes, it cannot be simplified further. 8. Approximate the value: $$c \approx 14.87$$ Therefore, the length of the hypotenuse is approximately 14.87 cm.