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Which of the following sets of numbers could not represent the three sides of a triangle? {7,17,22} {12,21,33} {10,12,20} {5,18,22}

Which of the following sets of numbers could not represent the three sides of a triangle?\newline{7,17,22} \{7,17,22\} \newline{12,21,33} \{12,21,33\} \newline{10,12,20} \{10,12,20\} \newline{5,18,22} \{5,18,22\}

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Checkpoint: Rational and irrational numbersright chevron icon

Full solution

Q. Which of the following sets of numbers could not represent the three sides of a triangle?\newline{7,17,22} \{7,17,22\} \newline{12,21,33} \{12,21,33\} \newline{10,12,20} \{10,12,20\} \newline{5,18,22} \{5,18,22\}
  1. 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.
  2. Check First Set: Check the first set of numbers {7,17,22}\{7,17,22\} to see if they satisfy the Triangle Inequality Theorem.7 + 17 > 22 (24 > 22) - True7 + 22 > 17 (29 > 17) - True17 + 22 > 7 (39 > 7) - TrueAll conditions are satisfied, so {7,17,22}\{7,17,22\} could represent the sides of a triangle.
  3. Check Second Set: Check the second set of numbers {12,21,33}\{12,21,33\} to see if they satisfy the Triangle Inequality Theorem.12 + 21 > 33 (33 > 33) - False, the sum is equal to the third side, not greater.12 + 33 > 21 (45 > 21) - True21 + 33 > 12 (54 > 12) - TrueThe first condition is not satisfied, so {12,21,33}\{12,21,33\} could not represent the sides of a triangle.
  4. Conclusion: Since we have found a set that does not satisfy the Triangle Inequality Theorem, we can conclude that {12,21,33}\{12,21,33\} could not represent the sides of a triangle. There is no need to check the remaining sets.

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