Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point)
8, 4, 12
20, 10, 30
10, 20, 15
8, 8, 20
To apply the Triangle Inequality Theorem, we need to check if the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
For the given side lengths:
1) 8, 4, 12:
8 + 4 = 12, which is less than 12. Therefore, these lengths do not form a triangle.
2) 20, 10, 30:
20 + 10 = 30, which is equal to 30. Therefore, these lengths do not form a triangle.
3) 10, 20, 15:
10 + 15 = 25, which is greater than 20.
10 + 20 = 30, which is greater than 15.
20 + 15 = 35, which is greater than 10.
Since the sum of the lengths of any two sides is greater than the length of the third side in all cases, the side lengths 10, 20, and 15 form a triangle.