Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point) Responses
10, 20, 15
20, 10, 30
8, 4, 12
8, 8, 20
The Triangle Inequality Theorem 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 (10, 20, 15):
- The sum of the shorter sides 10 and 15 is 25, which is greater than the longest side 20.
- The sum of the shorter sides 10 and 20 is 30, which is greater than the third side 15.
- The sum of the shorter sides 15 and 20 is 35, which is greater than the third side 10.
Therefore, the side lengths 10, 20, and 15 form a triangle.
2. For the second set of side lengths (20, 10, 30):
- The sum of the shorter sides 10 and 20 is 30, which is not greater than the longest side 30.
Therefore, the side lengths 20, 10, and 30 do not form a triangle.
3. For the third set of side lengths (8, 4, 12):
- The sum of the shorter sides 4 and 8 is 12, which is not greater than the longest side 12.
Therefore, the side lengths 8, 4, and 12 do not form a triangle.
4. For the fourth set of side lengths (8, 8, 20):
- The sum of the shorter sides 8 and 8 is 16, which is not greater than the longest side 20.
Therefore, the side lengths 8, 8, and 20 do not form a triangle.
In conclusion, only the side lengths 10, 20, and 15 form a triangle according to the Triangle Inequality Theorem.