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Which of the following sets of numbers could not represent the three sides of a triangle? {11,14,24} {12,21,33} {15,25,39} {10,22,31}

Which of the following sets of numbers could not represent the three sides of a triangle?\newline{11,14,24} \{11,14,24\} \newline{12,21,33} \{12,21,33\} \newline{15,25,39} \{15,25,39\} \newline{10,22,31} \{10,22,31\}

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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{11,14,24} \{11,14,24\} \newline{12,21,33} \{12,21,33\} \newline{15,25,39} \{15,25,39\} \newline{10,22,31} \{10,22,31\}
  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 Numbers: Check the first set of numbers {11,14,24}\{11, 14, 24\} to see if they satisfy the Triangle Inequality Theorem.\newline11 + 14 > 24 (25 > 24) - True\newline11 + 24 > 14 (35 > 14) - True\newline14 + 24 > 11 (38 > 11) - True\newlineAll conditions are satisfied, so {11,14,24}\{11, 14, 24\} could represent the sides of a triangle.
  3. Check Second Set Numbers: Check the second set of numbers 12,21,33{12, 21, 33} to see if they satisfy the Triangle Inequality Theorem.\newline12 + 21 > 33 (33 > 33) - False, the sum is equal to the third side, not greater.\newlineThis set does not satisfy the Triangle Inequality Theorem, so 12,21,33{12, 21, 33} cannot represent the sides of a triangle.
  4. Conclude Problem: Since we have already found a set that cannot represent the sides of a triangle, we do not need to check the remaining sets. We can conclude the problem here.

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