Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point)
Responses
10, 20, 15
10, 20, 15
20, 10, 30
20, 10, 30
8, 4, 12
8, 4, 12
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.
1. For 10, 20, 15: 10 + 15 > 20, 10 + 20 > 15, and 15 + 20 > 10. So, these side lengths form a triangle.
2. For 20, 10, 30: 20 + 10 > 30, 10 + 30 > 20, but 20 + 30 < 10 so these side lengths do not form a triangle.
3. For 8, 4, 12: 8 + 4 > 12, 4 + 12 > 8, but 8 + 12 < 4 so these side lengths do not form a triangle.
4. For 8, 8, 20: 8 + 8 > 20, but 8 + 20 < 8 and 8 + 20 < 8 so these side lengths do not form a triangle.
Therefore, the only set of side lengths that form a triangle is 10, 20, 15.