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Which of the following sets of numbers could not represent the three sides of a triangle? {14,27,40} {4,9,14} {9,21,29} {12,17,28}

Which of the following sets of numbers could not represent the three sides of a triangle?\newline{14,27,40} \{14,27,40\} \newline{4,9,14} \{4,9,14\} \newline{9,21,29} \{9,21,29\} \newline{12,17,28} \{12,17,28\}

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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{14,27,40} \{14,27,40\} \newline{4,9,14} \{4,9,14\} \newline{9,21,29} \{9,21,29\} \newline{12,17,28} \{12,17,28\}
  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 Set {14,27,40}\{14, 27, 40\}: Check the set {14,27,40}\{14, 27, 40\} to see if it satisfies the Triangle Inequality Theorem.\newlineCalculate if 14 + 27 > 40, 14 + 40 > 27, and 27 + 40 > 14.\newline14+27=4114 + 27 = 41 which is greater than 4040.\newline14+40=5414 + 40 = 54 which is greater than 2727.\newline27+40=6727 + 40 = 67 which is greater than {14,27,40}\{14, 27, 40\}00.\newlineAll conditions are satisfied, so this set could represent the sides of a triangle.
  3. Calculate Set {14,27,40}\{14, 27, 40\}: Check the set {4,9,14}\{4, 9, 14\} to see if it satisfies the Triangle Inequality Theorem.\newlineCalculate if 4 + 9 > 14, 4 + 14 > 9, and 9 + 14 > 4.\newline4+9=134 + 9 = 13 which is not greater than 1414.\newlineThis set does not satisfy the Triangle Inequality Theorem, so it cannot represent the sides of a triangle.

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