Question

which of the following sets of numbers could not represent the three sides of a triangle?
answer
{15,20,36} {6,19,22}
{13,26,37} {4,8,9}

Explanation:

Step1: Recall triangle inequality theorem

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

Step2: Check set \(\{15,20,36\}\)

Here \(a = 15\), \(b = 20\), \(c = 36\). Calculate \(a + b\): \(15+20=35\). Since \(35<36\) (i.e., \(a + b

Step3: Check set \(\{6,19,22\}\)

Here \(a = 6\), \(b = 19\), \(c = 22\). Calculate \(a + b\): \(6 + 19=25\). Since \(25>22\) (i.e., \(a + b>c\)).

Step4: Check set \(\{13,26,37\}\)

Here \(a = 13\), \(b = 26\), \(c = 37\). Calculate \(a + b\): \(13+26 = 39\). Since \(39>37\) (i.e., \(a + b>c\)).

Step5: Check set \(\{4,8,9\}\)

Here \(a = 4\), \(b = 8\), \(c = 9\). Calculate \(a + b\): \(4 + 8=12\). Since \(12>9\) (i.e., \(a + b>c\)).

Answer:

\(\{15,20,36\}\)