Question

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

Explanation:

Step1: Recall the triangle inequality theorem

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

Step2: Check the set \(\{12,19,32\}\)

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

Step3: Check the set \(\{8,14,24\}\)

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

Step4: Check the set \(\{5,15,21\}\)

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

Step5: Check the set \(\{14,24,36\}\)

Here \(a = 14\), \(b=24\), \(c = 36\). Then \(a + b=14+24=38\). Since \(38>36\), this set forms a triangle.

Answer:

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