Question

which of the following sets of numbers could represent the three sides of a triangle?
answer
{13,22,35} {6,18,22}
{5,13,19} {4,13,18}

Explanation:

Step1: Recall the 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 the set \(\{13,22,35\}\)

Here \(a = 13\), \(b=22\), \(c = 35\). Then \(a + b=13 + 22=35\), and \(35
ot>35\)

Step3: Check the set \(\{6,18,22\}\)

Here \(a = 6\), \(b = 18\), \(c=22\). Then \(a + b=6+18 = 24\), and \(24>22\)

Step4: Check the set \(\{5,13,19\}\)

Here \(a = 5\), \(b=13\), \(c = 19\). Then \(a + b=5 + 13=18\), and \(18
ot>19\)

Step5: Check the set \(\{4,13,18\}\)

Here \(a = 4\), \(b=13\), \(c = 18\). Then \(a + b=4+13 = 17\), and \(17
ot>18\)

Answer:

\(\{6,18,22\}\)