Question

which of the following sets of numbers could represent the three sides of a triangle? answer {11,26,38} {6,14,18} {15,17,34} {15,23,40} submit answer

Explanation:

Step1: Check triangle inequality for {11,26,38}

Check \(11 + 26>38\). \(11+26 = 37\), and \(37<38\). So, this set does not form a triangle.

Step2: Check triangle inequality for {6,14,18}

Check \(6 + 14>18\). \(6 + 14=20\), and \(20>18\). Then check \(6+18>14\) (\(6 + 18=24>14\)) and \(14 + 18>6\) (\(14+18 = 32>6\)).

Step3: Check triangle inequality for {15,17,34}

Check \(15+17>34\). \(15 + 17=32\), and \(32<34\). So, this set does not form a triangle.

Step4: Check triangle inequality for {15,23,40}

Check \(15+23>40\). \(15+23 = 38\), and \(38<40\). So, this set does not form a triangle.

Answer:

\(\{6,14,18\}\)