Question
Do the side lengths 22 cm, 20 cm, and 25 cm create a triangle? Explain.
Yes because all the inequalities you can write that relate the side lengths are true.
No because
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No because
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No because
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Answers
GPT-4o mini
To determine whether the side lengths 22 cm, 20 cm, and 25 cm can create a triangle, we can use the triangle inequality theorem. This theorem states that, for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's check the triangle inequalities for the given side lengths:
1. \(22 + 20 > 25\)
- \(42 > 25\) (True)
2. \(22 + 25 > 20\)
- \(47 > 20\) (True)
3. \(20 + 25 > 22\)
- \(45 > 22\) (True)
Since all three inequalities are true, we can conclude that:
**Yes, because all the inequalities you can write that relate the side lengths are true.**
Let's check the triangle inequalities for the given side lengths:
1. \(22 + 20 > 25\)
- \(42 > 25\) (True)
2. \(22 + 25 > 20\)
- \(47 > 20\) (True)
3. \(20 + 25 > 22\)
- \(45 > 22\) (True)
Since all three inequalities are true, we can conclude that:
**Yes, because all the inequalities you can write that relate the side lengths are true.**