1. The problem asks if a triangle can have sides of lengths 3, 7, and 9. 2. To determine this, we use the Triangle Inequality Theorem, which states that for any triangle with sides $a$, $b$, and $c$, the following must be true: $$a + b > c$$ $$a + c > b$$ $$b + c > a$$ 3. Let's check each inequality with the given sides: - $3 + 7 = 10 > 9$ (True) - $3 + 9 = 12 > 7$ (True) - $7 + 9 = 16 > 3$ (True) 4. Since all three inequalities hold true, the sides 3, 7, and 9 can form a triangle. **Final answer:** Yes, the sides 3, 7, and 9 can form a triangle.