Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle
responses
8, 4, 12
20, 10, 30
10, 20, 15
8, 8, 20
The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Applying this theorem, we can determine which three side lengths form a triangle:
1) 8, 4, 12: 8 + 4 = 12, which is not greater than 12. This set of side lengths does not form a triangle.
2) 20, 10, 30: 20 + 10 = 30, which is not greater than 30. This set of side lengths does not form a triangle.
3) 10, 20, 15: 10 + 15 = 25, which is greater than 20. Furthermore, 10 + 20 = 30, which is greater than 15. This set of side lengths does form a triangle.
4) 8, 8, 20: 8 + 8 = 16, which is not greater than 20. This set of side lengths does not form a triangle.
Therefore, only the side lengths of 10, 20, and 15 form a triangle.