Question

question
which of the following sets of numbers could not represent the three sides of a triangle?
answer
{14,16,28} {4,16,21}
{6,11,16} {8,20,27}

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 \(a + b\) must be greater than the longest side \(c\).

Step2: Check set \(\{14,16,28\}\)

\(14+16 = 30>28\)

Step3: Check set \(\{4,16,21\}\)

\(4 + 16=20<21\)

Step4: Check set \(\{6,11,16\}\)

\(6+11 = 17>16\)

Step5: Check set \(\{8,20,27\}\)

\(8+20=28>27\)

Answer:

\(\{4,16,21\}\)