Question

which of the following sets of numbers could not represent the three sides of a triangle?
answer
{12,22,35}
{10,22,30}
{13,17,29}
{6,9,14}
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Explanation:

Step1: Apply triangle inequality theorem

For a set of numbers \(a,b,c\) to be the sides of a triangle, the following three inequalities must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\).

Step2: Check \(\{6,9,14\}\)

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

Step3: Check \(\{10,22,30\}\)

\(10+22=32>30\), \(10 + 30=40>22\), \(22+30=52>10\).

Step4: Check \(\{12,22,35\}\)

\(12+22 = 34<35\).

Step5: Check \(\{13,17,29\}\)

\(13+17=30>29\), \(13 + 29=42>17\), \(17+29=46>13\).

Answer:

\(\{12,22,35\}\)