Question

which of the following sets of numbers could not represent the three sides of a triangle?
answer
{13,16,26} {8,17,22}
{5,9,16} {8,13,18}

Explanation:

Step1: Recall triangle inequality theorem

For three side lengths \(a\), \(b\), \(c\) (\(a\leq b\leq c\)), the triangle inequality theorem states that \(a + b>c\).

Step2: Check set \(\{5,9,16\}\)

Here \(a = 5\), \(b=9\), \(c = 16\). Calculate \(a + b\): \(5+9=14\). Since \(14<16\) (i.e., \(a + b

Step3: Check set \(\{13,16,26\}\)

Let \(a = 13\), \(b = 16\), \(c=26\). Then \(a + b=13 + 16=29>26\).

Step4: Check set \(\{8,17,22\}\)

Let \(a = 8\), \(b = 17\), \(c=22\). Then \(a + b=8 + 17=25>22\).

Step5: Check set \(\{8,13,18\}\)

Let \(a = 8\), \(b = 13\), \(c=18\). Then \(a + b=8+13 = 21>18\).

Answer:

\(\{5,9,16\}\)