Question

which of the following sets of numbers could not represent the three sides of a triangle?
answer
{6,9,14}
{6,11,16}
{6,16,21}
{12,17,30}
submit answer

Explanation:

Step1: Check triangle inequality for {6,9,14}

Check if \(6 + 9>14\), \(6+14 > 9\), \(9 + 14>6\).
\(6+9=15>14\), \(6 + 14=20>9\), \(9+14 = 23>6\).

Step2: Check triangle inequality for {6,11,16}

Check if \(6+11>16\), \(6 + 16>11\), \(11+16>6\).
\(6+11 = 17>16\), \(6+16=22>11\), \(11 + 16=27>6\).

Step3: Check triangle inequality for {6,16,21}

Check if \(6+16>21\), \(6+21>16\), \(16+21>6\).
\(6+16=22>21\), \(6+21 = 27>16\), \(16+21=37>6\).

Step4: Check triangle inequality for {12,17,30}

Check if \(12 + 17>30\), \(12+30>17\), \(17+30>12\).
\(12+17=29<30\), \(12+30=42>17\), \(17+30=47>12\).

Answer:

\(\{12,17,30\}\)