Question
Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point)
Responses
8, 4, 12
8, 4, 12
10, 20, 15
10, 20, 15
20, 10, 30
20, 10, 30
8, 8, 20
Responses
8, 4, 12
8, 4, 12
10, 20, 15
10, 20, 15
20, 10, 30
20, 10, 30
8, 8, 20
Answers
Answered by
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:
1. 8 + 4 = 12, which is greater than 12. 12 + 8 = 20, which is greater than 4. 12 + 4 = 16, which is greater than 8. Therefore, 8, 4, and 12 form a triangle.
2. 10 + 20 = 30, which is greater than 15. 20 + 15 = 35, which is greater than 10. 10 + 15 = 25, which is greater than 20. Therefore, 10, 20, and 15 form a triangle.
3. 20 + 10 = 30, which is greater than 20. 10 + 30 = 40, which is greater than 20. 20 + 30 = 50, which is greater than 10. Therefore, 20, 10, and 30 form a triangle.
4. 8 + 8 = 16, which is not greater than 20. Therefore, 8, 8, and 20 do not form a triangle.
Applying this theorem:
1. 8 + 4 = 12, which is greater than 12. 12 + 8 = 20, which is greater than 4. 12 + 4 = 16, which is greater than 8. Therefore, 8, 4, and 12 form a triangle.
2. 10 + 20 = 30, which is greater than 15. 20 + 15 = 35, which is greater than 10. 10 + 15 = 25, which is greater than 20. Therefore, 10, 20, and 15 form a triangle.
3. 20 + 10 = 30, which is greater than 20. 10 + 30 = 40, which is greater than 20. 20 + 30 = 50, which is greater than 10. Therefore, 20, 10, and 30 form a triangle.
4. 8 + 8 = 16, which is not greater than 20. Therefore, 8, 8, and 20 do not form a triangle.