To determine which side length would not create a triangle with sides measuring 11 and 3, we can apply the triangle inequality theorem. This theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), the following conditions must be met:
- \(a + b > c\)
- \(a + c > b\)
- \(b + c > a\)
In this scenario, let's denote the sides as \(a = 11\), \(b = 3\), and \(c\) as the unknown side. We'll analyze each of the potential side lengths provided as responses.
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When \(c = 9\):
- \(11 + 3 > 9\) (True: 14 > 9)
- \(11 + 9 > 3\) (True: 20 > 3)
- \(3 + 9 > 11\) (True: 12 > 11)
- This is a valid triangle.
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When \(c = 7\):
- \(11 + 3 > 7\) (True: 14 > 7)
- \(11 + 7 > 3\) (True: 18 > 3)
- \(3 + 7 > 11\) (False: 10 is not greater than 11)
- This does NOT form a valid triangle.
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When \(c = 13\):
- \(11 + 3 > 13\) (False: 14 is not greater than 13)
- \(11 + 13 > 3\) (True: 24 > 3)
- \(3 + 13 > 11\) (True: 16 > 11)
- This does NOT form a valid triangle.
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When \(c = 12\):
- \(11 + 3 > 12\) (False: 14 is not greater than 12)
- \(11 + 12 > 3\) (True: 23 > 3)
- \(3 + 12 > 11\) (True: 15 > 11)
- This does NOT form a valid triangle.
From the analysis, we find that the side lengths \(7\), \(13\), and \(12\) do not create a triangle. However, from the provided responses, the side measure that will definitely not create a triangle is:
7
1 answer