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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.
- Apply Theorem to Set : Apply the Triangle Inequality Theorem to the first set of numbers . Check if , , and . Calculations: , , . Since is not greater than , the first set does not satisfy the Triangle Inequality Theorem.
- Apply Theorem to Set : Apply the Triangle Inequality Theorem to the second set of numbers . Check if , , and . Calculations: , , . Since is not greater than , the second set does not satisfy the Triangle Inequality Theorem.
- Apply Theorem to Set : Apply the Triangle Inequality Theorem to the third set of numbers .Check if , , and .Calculations: , , .All sums are greater than the third side, so the third set satisfies the Triangle Inequality Theorem.
- Apply Theorem to Set : Apply the Triangle Inequality Theorem to the fourth set of numbers . Check if , , and . Calculations: , , . Since is not greater than , the fourth set does not satisfy the Triangle Inequality Theorem.
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