Question
Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.
Pick one of the answers
1. 8, 8, 20
2. 10, 20, 15
3. 20, 10, 30
4. 8, 4, 12
Pick one of the answers
1. 8, 8, 20
2. 10, 20, 15
3. 20, 10, 30
4. 8, 4, 12
Answers
Bot
The Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than the third side.
Using this theorem, we can eliminate option 1 (8, 8, 20) because 8 + 8 is only 16, which is not greater than 20.
We can also eliminate option 4 (8, 4, 12) because 4 + 8 is only 12, which is not greater than 12.
Therefore, the answer is option 2 (10, 20, 15) and option 3 (20, 10, 30) because in both cases, the sum of any two sides is greater than the third side.
Using this theorem, we can eliminate option 1 (8, 8, 20) because 8 + 8 is only 16, which is not greater than 20.
We can also eliminate option 4 (8, 4, 12) because 4 + 8 is only 12, which is not greater than 12.
Therefore, the answer is option 2 (10, 20, 15) and option 3 (20, 10, 30) because in both cases, the sum of any two sides is greater than the third side.