Question

which of the following sets of numbers could not represent the three sides of a triangle? answer {5,11,13} {15,25,42} {10,20,29} {12,22,32}

Explanation:

Step1: Check triangle inequality for {5, 11, 13}

Check \(5 + 11>13\) (\(16>13\)), \(5 + 13>11\) (\(18>11\)), \(11 + 13>5\) (\(24>5\)).

Step2: Check triangle inequality for {15, 25, 42}

Check \(15 + 25>42\). \(15+25 = 40\), and \(40<42\).

Step3: Check triangle inequality for {10, 20, 29}

Check \(10 + 20>29\) (\(30>29\)), \(10 + 29>20\) (\(39>20\)), \(20 + 29>10\) (\(49>10\)).

Step4: Check triangle inequality for {12, 22, 32}

Check \(12 + 22>32\). \(12 + 22=34\), \(34>32\), \(12+32>22\) (\(44>22\)), \(22 + 32>12\) (\(54>12\)).

Answer:

\(\{15,25,42\}\)