Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.

Question

Pick one of the answers There is only one answer.
1. 8, 8, 20
2. 10, 20, 15
3. 20, 10, 30
4. 8, 4, 12

Answer 1

The answer is 2. 10, 20, 15.

According to the Triangle Inequality Theorem, the sum of any two sides of a triangle must be greater than the third side.

Let's check each set of side lengths:

1. 8 + 8 = 16, which is less than 20. Therefore, these side lengths do not form a triangle.
2. 10 + 20 = 30, 10 + 15 = 25, and 20 + 15 = 35. All of these sums are greater than the third side, so these side lengths do form a triangle.
3. 20 + 10 = 30, which is less than 30. Therefore, these side lengths do not form a triangle.
4. 8 + 4 = 12, which is equal to the third side. Therefore, these side lengths do not form a triangle.