1. **Stating the problem:** We are given three triangles with side lengths: - Top triangle: 7, 7, 25 - Middle triangle: 3, 4, 24 - Bottom triangle: 6, 6, 12 We need to analyze these triangles, check if they are valid triangles, and understand their properties. 2. **Triangle inequality rule:** For any triangle with sides $a$, $b$, and $c$, the sum of any two sides must be greater than the third side: $$a + b > c, \quad a + c > b, \quad b + c > a$$ 3. **Check the top triangle (7, 7, 25):** - $7 + 7 = 14$ which is not greater than $25$ - This violates the triangle inequality, so the top triangle is **not a valid triangle**. 4. **Check the middle triangle (3, 4, 24):** - $3 + 4 = 7$ which is not greater than $24$ - This violates the triangle inequality, so the middle triangle is **not a valid triangle**. 5. **Check the bottom triangle (6, 6, 12):** - $6 + 6 = 12$ which is equal to $12$ - The sum of two sides equals the third side, so this is a **degenerate triangle** (it forms a straight line, not a triangle with area). **Final conclusion:** - The top and middle sets of side lengths do not form valid triangles. - The bottom set forms a degenerate triangle. Hence, none of the given side lengths form a proper triangle with area.