Question
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
responses
8, 4, 12
20, 10, 30
10, 20, 15
8, 8, 20
Answers
GPT 3.5
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.
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.