To determine which three side lengths form a triangle using the Triangle Inequality Theorem, we need to check if the sum of the two shorter sides is greater than the longest side.
A. For side lengths 8, 4, 12:
8 + 4 = 12, which is not greater than 12. Therefore, these side lengths do not form a triangle.
B. For side lengths 20, 10, 30:
10 + 20 = 30, which is equal to 30. Therefore, these side lengths do not form a triangle.
C. For side lengths 10, 20, 15:
10 + 15 = 25, which is greater than 20 and 15 + 20 = 35 is greater than 10. Therefore, these side lengths form a triangle.
D. For side lengths 8, 8, 20:
8 + 8 = 16, which is not greater than 20. Therefore, these side lengths do not form a triangle.
Therefore, only side lengths 10, 20, 15 form a triangle according to the Triangle Inequality Theorem. So the answer is C. 10, 20, 15.
Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point)
Responses
A. 8, 4, 12
B. 20, 10, 30
C. 10, 20, 15
D. 8, 8, 20
1 answer
1 answer