1. **Problem statement:** We have a triangle with two sides of lengths 9 and 19. We want to find the largest possible whole-number length for the third side. 2. **Formula and rule:** For any triangle with sides $a$, $b$, and $c$, the triangle inequality states: $$a + b > c, \quad b + c > a, \quad c + a > b$$ This means the sum of the lengths of any two sides must be greater than the length of the third side. 3. **Apply the triangle inequality:** Let the third side be $x$. We know two sides are 9 and 19. - $9 + 19 > x \implies 28 > x$ - $9 + x > 19 \implies x > 10$ - $19 + x > 9 \implies x > -10$ (always true since $x$ is positive) 4. **Combine inequalities:** From above, $10 < x < 28$. 5. **Find largest whole number:** The largest whole number less than 28 and greater than 10 is 27. **Final answer:** The largest possible whole-number length for the third side is **27**.