Question

Apply the Triangle inequality Theorem to determine which three side from a triangle.

20,10,30
8,8,20
8,4,12
10,20,15

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine if the three given side lengths can form a triangle, we need to 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.

1. For the first set of side lengths 20, 10, 30:
- 20 + 10 > 30 (True)
- 20 + 30 > 10 (True)
- 10 + 30 > 20 (True)
Therefore, these side lengths can form a triangle.

2. For the second set of side lengths 8, 8, 20:
- 8 + 8 > 20 (False)
Therefore, these side lengths cannot form a triangle.

3. For the third set of side lengths 8, 4, 12:
- 8 + 4 > 12 (False)
Therefore, these side lengths cannot form a triangle.

4. For the fourth set of side lengths 10, 20, 15:
- 10 + 20 > 15 (True)
- 10 + 15 > 20 (True)
- 20 + 15 > 10 (True)
Therefore, these side lengths can form a triangle.

In conclusion,
- The three side lengths from the first set (20, 10, 30) can form a triangle.
- The three side lengths from the second set (8, 8, 20) cannot form a triangle.
- The three side lengths from the third set (8, 4, 12) cannot form a triangle.
- The three side lengths from the fourth set (10, 20, 15) can form a triangle.