Question

question
which of the following sets of numbers could represent the three sides of a triangle?
answer
{5,13,19} {5,17,23}
{4,17,22} {15,22,36}

Explanation:

Step1: Recall triangle inequality theorem

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

Step2: Check set \(\{5,13,19\}\)

Here \(a = 5\), \(b = 13\), \(c=19\). Then \(a + b=5 + 13=18\), and \(18<19\). So this set does not form a triangle.

Step3: Check set \(\{5,17,23\}\)

Here \(a = 5\), \(b = 17\), \(c = 23\). Then \(a + b=5+17 = 22\), and \(22<23\). So this set does not form a triangle.

Step4: Check set \(\{4,17,22\}\)

Here \(a = 4\), \(b = 17\), \(c = 22\). Then \(a + b=4 + 17=21\), and \(21<22\). So this set does not form a triangle.

Step5: Check set \(\{15,22,36\}\)

Here \(a = 15\), \(b = 22\), \(c = 36\). Then \(a + b=15+22 = 37\), and \(37>36\).

Answer:

\(\{15,22,36\}\)