Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point) Responses 8, 4, 12
20, 10, 30
10, 20,15
8,8,20
pls answer correctly
To determine if three side lengths form a triangle, we can use 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.
Applying the theorem to the given sets of side lengths:
1) 8, 4, 12: The sum of 8 and 4 is 12, which is less than 12. Therefore, this set of side lengths does not form a triangle.
2) 20, 10, 30: The sum of 20 and 10 is 30, which is equal to 30. According to the Triangle Inequality Theorem, the sum of any two sides must be greater than the length of the third side. Hence, this set of side lengths does not form a triangle.
3) 10, 20, 15: The sum of 10 and 15 is 25, which is greater than 20. The sum of 10 and 20 is 30, which is also greater than 15. And finally, the sum of 20 and 15 is 35, which is greater than 10. Thus, this set of side lengths does form a triangle.
4) 8, 8, 20: The sum of 8 and 8 is 16, which is less than 20. Since the sum of any two sides must be greater than the length of the third side, this set of side lengths does not form a triangle.
Therefore, the only set of side lengths that form a triangle is 10, 20, 15.