For 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, 26, 1610 , 5, 168 , 5.3, 6.812.7 , 7, 86
Question
For 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, 26, 1610 , 5, 168 , 5.3, 6.812.7 , 7, 86
Solution
To determine if three lengths can form a triangle, we 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 each set of lengths:
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26, 16, 10: 26 + 16 > 10 (True) 26 + 10 > 16 (True) 16 + 10 > 26 (False) Since all conditions are not true, these lengths cannot form a triangle.
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5, 16, 8: 5 + 16 > 8 (True) 5 + 8 > 16 (False) 16 + 8 > 5 (True) Since all conditions are not true, these lengths cannot form a triangle.
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5.3, 6.8, 12.7: 5.3 + 6.8 > 12.7 (False) 5.3 + 12.7 > 6.8 (True) 6.8 + 12.7 > 5.3 (True) Since all conditions are not true, these lengths cannot form a triangle.
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7, 8, 6: 7 + 8 > 6 (True) 7 + 6 > 8 (True) 8 + 6 > 7 (True) Since all conditions are true, these lengths can form a triangle.
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