Question

Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point) Responses 20, 10, 30 20, 10, 30 8, 8, 20 8, 8, 20 8, 4, 12 8, 4, 12 10, 20, 15

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine which three side lengths form a triangle, we apply the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's check each set of side lengths:

1. 20, 10, 30
20 + 10 > 30 (True)
20 + 30 > 10 (True)
10 + 30 > 20 (True)

Therefore, the side lengths 20, 10, 30 form a triangle.

2. 8, 8, 20
8 + 8 > 20 (False)

Therefore, the side lengths 8, 8, 20 do not form a triangle.

3. 8, 4, 12
8 + 4 > 12 (True)
8 + 12 > 4 (True)
4 + 12 > 8 (True)

Therefore, the side lengths 8, 4, 12 form a triangle.

4. 10, 20, 15
10 + 20 > 15 (True)
10 + 15 > 20 (True)
20 + 15 > 10 (True)

Therefore, the side lengths 10, 20, 15 form a triangle.

So, the three side lengths that form a triangle are 20, 10, 30 and 10, 20, 15.