Question

which of the following sets of numbers could not represent the three sides of a triangle?
answer
{5,11,13}
{10,20,29}
{15,25,42}
{12,22,32}

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

Step2: Check \(\{5,11,13\}\)

Here \(a = 5\), \(b=11\), \(c = 13\). Then \(a + b=5 + 11=16\), and \(16>13\).

Step3: Check \(\{10,20,29\}\)

Here \(a = 10\), \(b = 20\), \(c=29\). Then \(a + b=10+20 = 30\), and \(30>29\).

Step4: Check \(\{15,25,42\}\)

Here \(a = 15\), \(b = 25\), \(c = 42\). Then \(a + b=15+25=40\), and \(40<42\).

Step5: Check \(\{12,22,32\}\)

Here \(a = 12\), \(b = 22\), \(c = 32\). Then \(a + b=12 + 22=34\), and \(34>32\).

Answer:

\(\{15,25,42\}\)