Question

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

Answer 1

it can only be one of the answers

Answer 2

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.

Let's apply this theorem to the given side lengths:
1. 10, 20, 15
10 + 15 = 25 > 20, 10 + 20 = 30 > 15, 15 + 20 = 35 > 10
These side lengths can form a triangle.

2. 8, 8, 20
8 + 8 = 16 < 20, 8 + 20 = 28 > 8, 8 + 20 = 28 > 8
These side lengths cannot form a triangle.

3. 20, 10, 30
20 + 10 = 30 > 30, 20 + 30 = 50 > 10, 10 + 30 = 40 > 20
These side lengths can form a triangle.

4. 8, 4, 12
8 + 4 = 12 < 12, 8 + 12 = 20 > 4, 4 + 12 = 16 > 8
These side lengths can form a triangle.

Therefore, the three side lengths that form a triangle are:
10, 20, 15
20, 10, 30
8, 4, 12

Answer 3

Apologies for the oversight. Let's correct the answer based on the Triangle Inequality Theorem:

The only set of side lengths that form a triangle according to the Triangle Inequality Theorem is:
10, 20, 15

Therefore, the response is:
10, 20, 15