1. **State the problem:** We have a triangle with two sides of lengths 12 and 16. We want to find the largest possible whole-number length for the third side. 2. **Recall the triangle inequality rule:** For any triangle with sides $a$, $b$, and $c$, the sum of the lengths of any two sides must be greater than the length of the third side. This gives us three inequalities: $$a + b > c$$ $$a + c > b$$ $$b + c > a$$ 3. **Apply the inequalities to our sides:** Let the third side be $x$. Then: - $12 + 16 > x \implies 28 > x$ - $12 + x > 16 \implies x > 4$ - $16 + x > 12 \implies x > -4$ (which is always true since side lengths are positive) 4. **Combine the inequalities:** The third side $x$ must satisfy: $$4 < x < 28$$ 5. **Find the largest whole number:** The largest whole number less than 28 is 27. **Final answer:** The largest possible whole-number length for the third side is **27**.