1. The problem asks if a triangle can have sides of lengths 17.5, 18.8, and 5.7. 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: - $17.5 + 18.8 = 36.3 > 5.7$ (True) - $17.5 + 5.7 = 23.2 > 18.8$ (True) - $18.8 + 5.7 = 24.5 > 17.5$ (True) 4. Since all three inequalities hold true, the side lengths satisfy the Triangle Inequality Theorem. 5. Therefore, a triangle with sides 17.5, 18.8, and 5.7 can exist.