1. **Problem:** Determine if the side lengths 10 ft, 12 ft, and 25 ft can form a triangle. 2. **Triangle Inequality Theorem:** For any triangle with sides $a$, $b$, and $c$, the following must hold true: $$a + b > c$$ $$a + c > b$$ $$b + c > a$$ This means the sum of any two sides must be greater than the third side. 3. **Apply the theorem:** - Check $10 + 12 > 25$: $$10 + 12 = 22 \not> 25$$ - Check $10 + 25 > 12$: $$10 + 25 = 35 > 12$$ - Check $12 + 25 > 10$: $$12 + 25 = 37 > 10$$ 4. Since $10 + 12 \not> 25$, the triangle inequality fails. 5. **Conclusion:** The side lengths 10 ft, 12 ft, and 25 ft cannot form a triangle because the sum of the two smaller sides is not greater than the largest side. **Final answer:** No, these side lengths do not form a triangle.