Question
Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.
Pick one of the answers There is only one answer.
1. 8, 8, 20
2. 10, 20, 15
3. 20, 10, 30
4. 8, 4, 12
Pick one of the answers There is only one answer.
1. 8, 8, 20
2. 10, 20, 15
3. 20, 10, 30
4. 8, 4, 12
Answers
Bot
The answer is 2. 10, 20, 15.
According to the Triangle Inequality Theorem, the sum of any two sides of a triangle must be greater than the third side.
Let's check each set of side lengths:
1. 8 + 8 = 16, which is less than 20. Therefore, these side lengths do not form a triangle.
2. 10 + 20 = 30, 10 + 15 = 25, and 20 + 15 = 35. All of these sums are greater than the third side, so these side lengths do form a triangle.
3. 20 + 10 = 30, which is less than 30. Therefore, these side lengths do not form a triangle.
4. 8 + 4 = 12, which is equal to the third side. Therefore, these side lengths do not form a triangle.
According to the Triangle Inequality Theorem, the sum of any two sides of a triangle must be greater than the third side.
Let's check each set of side lengths:
1. 8 + 8 = 16, which is less than 20. Therefore, these side lengths do not form a triangle.
2. 10 + 20 = 30, 10 + 15 = 25, and 20 + 15 = 35. All of these sums are greater than the third side, so these side lengths do form a triangle.
3. 20 + 10 = 30, which is less than 30. Therefore, these side lengths do not form a triangle.
4. 8 + 4 = 12, which is equal to the third side. Therefore, these side lengths do not form a triangle.