To determine which three side lengths form a triangle, we need to check if the sum of the lengths of any two sides is greater than the length of the third side.
1. For side lengths 2, 7, 9:
2 + 7 = 9, which is less than 9. This violates the Triangle Inequality Theorem, so these side lengths do not form a triangle.
2. For side lengths 7, 8, 9:
7 + 8 = 15, which is greater than 9.
8 + 9 = 17, which is greater than 7.
7 + 9 = 16, which is greater than 8.
Therefore, these side lengths can form a triangle.
3. For side lengths 7, 5, 13:
7 + 5 = 12, which is less than 13. This violates the Triangle Inequality Theorem, so these side lengths do not form a triangle.
4. For side lengths 4, 15, 20:
4 + 15 = 19, which is less than 20. This violates the Triangle Inequality Theorem, so these side lengths do not form a triangle.
Therefore, only the side lengths 7, 8, 9 form a triangle.
Use the Triangle Inequality Theorem to determine which three side lengths form a triangle.
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1 point
2, 7, 9
7, 8, 9
7, 5, 13
4, 15, 20
1 answer
1 answer