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or each set of three lengths, determine if they can be the side lengths of a triangle.Lengths Can be side lengths of a triangle Cannot be side lengths of a triangle, 18, 610 , 9.1, 3.56.3 , 7, 724 , 14, 73

Question

or each set of three lengths, determine if they can be the side lengths of a triangle.Lengths Can be side lengths of a triangle Cannot be side lengths of a triangle, 18, 610 , 9.1, 3.56.3 , 7, 724 , 14, 73

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Solution

The text you provided seems to be a bit jumbled, but I'll do my best to answer your question.

To determine if three lengths can form a triangle, you 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 apply this to the sets of lengths you provided:

  1. 18, 6, 10: 18 + 6 > 10 and 18 + 10 > 6 and 6 + 10 > 18. All these inequalities are true, so these lengths can form a triangle.

  2. 9.1, 3.5, 6.3: 9.1 + 3.5 > 6.3 and 9.1 + 6.3 > 3.5 and 3.5 + 6.3 > 9.1. All these inequalities are true, so these lengths can form a triangle.

  3. 7, 7, 24: 7 + 7 > 24 but 7 + 24 is not greater than 7 and 7 + 24 is not greater than 7. Since not all these inequalities are true, these lengths cannot form a triangle.

  4. 14, 7, 3: 14 + 7 > 3 and 14 + 3 > 7 and 7 + 3 > 14. Not all these inequalities are true, so these lengths cannot form a triangle.

This problem has been solved

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