Question

Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point)

Responses

10, 20, 15
10, 20, 15

20, 10, 30
20, 10, 30

8, 4, 12
8, 4, 12

8, 8, 20

Answer 1

[AI-generated answer — Bot 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.

1. For 10, 20, 15: 10 + 15 > 20, 10 + 20 > 15, and 15 + 20 > 10. So, these side lengths form a triangle.

2. For 20, 10, 30: 20 + 10 > 30, 10 + 30 > 20, but 20 + 30 < 10 so these side lengths do not form a triangle.

3. For 8, 4, 12: 8 + 4 > 12, 4 + 12 > 8, but 8 + 12 < 4 so these side lengths do not form a triangle.

4. For 8, 8, 20: 8 + 8 > 20, but 8 + 20 < 8 and 8 + 20 < 8 so these side lengths do not form a triangle.

Therefore, the only set of side lengths that form a triangle is 10, 20, 15.