1. **State the problem:** We need to find the length of the hypotenuse $c$ of a right triangle with legs of lengths 11 and 5. 2. **Formula used:** The Pythagorean Theorem states that for 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. **Apply the formula:** Here, $a = 11$ and $b = 5$, so: $$c^2 = 11^2 + 5^2$$ 4. **Calculate squares:** $$c^2 = 121 + 25$$ 5. **Sum the squares:** $$c^2 = 146$$ 6. **Find $c$ by taking the square root:** $$c = \sqrt{146}$$ 7. **Simplify if possible:** 146 factors as $2 \times 73$, both prime, so it cannot be simplified further. 8. **Final answer:** $$c = \sqrt{146} \approx 12.08$$ This means the hypotenuse length is approximately 12.08 units.