Question

Unit 4 Relearning Test 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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine which 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.

Let's test each set of side lengths:

1. 2, 7, 9
2 + 7 = 9, which is equal to the third side. Therefore, this set of side lengths does not form a triangle.

2. 7, 8, 9
7 + 8 = 15, which is greater than 9.
7 + 9 = 16, which is greater than 8.
8 + 9 = 17, which is greater than 7.
Therefore, this set of side lengths can form a triangle.

3. 7, 5, 13
7 + 5 = 12, which is less than 13.
Therefore, this set of side lengths does not form a triangle.

4. 4, 15, 20
4 + 15 = 19, which is less than 20.
Therefore, this set of side lengths does not form a triangle.

Based on the Triangle Inequality Theorem, the three side lengths that form a triangle are 7, 8, and 9.