Question

question: which of the following sets of numbers could represent the three sides of a triangle? answer: {15,19,34} {9,13,19} {8,20,30} {9,24,34}

Explanation:

Step1: Recall triangle - inequality theorem

For three side - lengths \(a\), \(b\), and \(c\) of a triangle, \(a + b>c\), \(a + c>b\), and \(b + c>a\).

Step2: Check {15,19,34}

\(15+19 = 34\), which does not satisfy \(a + b>c\) (here \(a = 15\), \(b = 19\), \(c = 34\)).

Step3: Check {9,13,19}

\(9 + 13=22>19\), \(9+19 = 28>13\), \(13 + 19=32>9\), satisfies the theorem.

Step4: Check {8,20,30}

\(8+20 = 28<30\), does not satisfy the theorem.

Step5: Check {9,24,34}

\(9+24 = 33<34\), does not satisfy the theorem.

Answer:

{9,13,19}