Apply the Triangle Inequality Theorem to determine
which three side lengths form a triangle. (1 point)
8, 4, 12
8, 8, 20
20, 10, 30
10, 20, 15
The Triangle Inequality Theorem states that for any three side lengths, the sum of the lengths of any two sides must be greater than the length of the third side in order for a triangle to be formed.
Now, let's check the given choices:
1) 8, 4, 12:
8 + 4 = 12, which is not greater than 12. So, a triangle cannot be formed with these side lengths.
2) 8, 8, 20:
8 + 8 = 16, which is not greater than 20. So, a triangle cannot be formed with these side lengths.
3) 20, 10, 30:
20 + 10 = 30, which is equal to 30. According to the Triangle Inequality Theorem, the sum of the lengths of any two sides must be greater than the length of the third side. Since the sum here is equal to the third side, a triangle cannot be formed with these side lengths.
4) 10, 20, 15:
10 + 15 = 25, which is greater than 20.
10 + 20 = 30, which is greater than 15.
15 + 20 = 35, which is greater than 10.
For this set, the sum of the lengths of any two sides is greater than the length of the third side. Therefore, a triangle can be formed with these side lengths.
In conclusion, the three side lengths that form a triangle are 10, 20, and 15.