Question

which of the following sets of numbers could not represent the three sides of a triangle?
answer
{14,19,32} {6,20,26}
{15,27,41} {13,18,30}

Explanation:

Step1: Check triangle inequality for {14,19,32}

Check if \(14 + 19>32\). Calculate \(14+19 = 33\), and \(33>32\). Also check \(14 + 32>19\) (\(46>19\)) and \(19+32>14\) (\(51>14\)).

Step2: Check triangle inequality for {6,20,26}

Check if \(6 + 20>26\). Calculate \(6 + 20=26\), and \(26
ot>26\).

Step3: Check triangle inequality for {15,27,41}

Check if \(15+27>41\). Calculate \(15 + 27=42\), and \(42>41\). Also check \(15 + 41>27\) (\(56>27\)) and \(27+41>15\) (\(68>15\)).

Step4: Check triangle inequality for {13,18,30}

Check if \(13+18>30\). Calculate \(13 + 18=31\), and \(31>30\). Also check \(13 + 30>18\) (\(43>18\)) and \(18+30>13\) (\(48>13\)).

Answer:

\(\{6,20,26\}\)