Question

question which of the following sets of numbers could represent the three sides of a triangle? answer {12, 19, 32} {8, 14, 24} {14, 24, 36} {5, 15, 21}

Explanation:

Step1: Apply triangle inequality theorem

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

For the set \(\{5,15,21\}\)

Let \(a = 5\), \(b = 15\), \(c=21\). Then \(a + b=5 + 15=20\), and \(20<21\). So, this set does not form a triangle.

For the set \(\{12,19,32\}\)

Let \(a = 12\), \(b = 19\), \(c = 32\). Then \(a + b=12+19 = 31\), and \(31<32\). So, this set does not form a triangle.

For the set \(\{8,14,24\}\)

Let \(a = 8\), \(b = 14\), \(c = 24\). Then \(a + b=8 + 14=22\), and \(22<24\). So, this set does not form a triangle.

For the set \(\{14,24,36\}\)

Let \(a = 14\), \(b = 24\), \(c = 36\). Then \(a + b=14+24 = 38\), and \(38>36\)

Answer:

\(\{14,24,36\}\)