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Which of the following sets of numbers could represent the three sides of a triangle?
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Q. Which of the following sets of numbers could represent the three sides of a triangle?
- Recall Triangle Inequality Theorem: Recall 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.
- Test First Set: Test the first set of numbers to see if they satisfy the Triangle Inequality Theorem.Check if , which is . This is not true, so the set cannot represent the sides of a triangle.
- Test Second Set: Test the second set of numbers to see if they satisfy the Triangle Inequality Theorem.Check if , which is . This is not true, so the set cannot represent the sides of a triangle.
- Test Third Set: Test the third set of numbers to see if they satisfy the Triangle Inequality Theorem.Check if , which is . This is not true, so the set cannot represent the sides of a triangle.
- Test Fourth Set: Test the fourth set of numbers to see if they satisfy the Triangle Inequality Theorem.Check if , which is . This is true.Check if , which is . This is true.Check if , which is . This is true.Since all conditions of the Triangle Inequality Theorem are satisfied, the set can represent the sides of a triangle.
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