Question

which of the following sets of numbers could not represent the three sides of a triangle? answer {9,14,25} {6,14,19} {11,25,33} {8,18,24}

Explanation:

Step1: Check triangle inequality for {9,14,25}

Check if \(9 + 14>25\). Calculate \(9+14 = 23\). Since \(23<25\), the triangle inequality fails.

Step2: Check triangle inequality for {6,14,19}

Check \(6 + 14>19\). \(6+14=20>19\), \(6 + 19>14\) (\(6+19 = 25>14\)), \(14+19>6\) (\(14 + 19=33>6\)).

Step3: Check triangle inequality for {11,25,33}

Check \(11+25>33\). \(11 + 25=36>33\), \(11+33>25\) (\(11+33 = 44>25\)), \(25+33>11\) (\(25+33=58>11\)).

Step4: Check triangle inequality for {8,18,24}

Check \(8+18>24\). \(8 + 18=26>24\), \(8+24>18\) (\(8+24=32>18\)), \(18+24>8\) (\(18+24 = 42>8\)).

Answer:

\(\{9,14,25\}\)