Question

which of the following sets of numbers could represent the three sides of a triangle? answer {14,24,38} {6,11,17} {15,18,32} {8,11,19}

Explanation:

Step1: Recall triangle inequality theorem

For three side lengths \(a\), \(b\), \(c\) (\(a\leq b\leq c\)), the sum of the two shorter sides \(a + b>c\)

Step2: Check set \(\{14,24,38\}\)

\(14 + 24=38\), since \(14 + 24
ot>38\), this is not a triangle.

Step3: Check set \(\{6,11,17\}\)

\(6+11 = 17\), since \(6 + 11
ot>17\), this is not a triangle.

Step4: Check set \(\{15,18,32\}\)

\(15+18=33\), and \(33>32\)

Step5: Check set \(\{8,11,19\}\)

\(8 + 11=19\), since \(8+11
ot>19\), this is not a triangle.

Answer:

\(\{15,18,32\}\)