Question

which of the following sets of numbers could represent the three sides of a triangle? answer {12,24,37} {12,24,38} {8,15,21} {12,20,32}

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 \(\{8,15,21\}\)

Here \(a = 8\), \(b=15\), \(c = 21\). Calculate \(a + b=8 + 15=23\). Since \(23>21\).

Step3: Check set \(\{12,24,37\}\)

Here \(a = 12\), \(b = 24\), \(c=37\). Calculate \(a + b=12+24 = 36\). Since \(36<37\).

Step4: Check set \(\{12,24,38\}\)

Here \(a = 12\), \(b = 24\), \(c = 38\). Calculate \(a + b=12 + 24=36\). Since \(36<38\).

Step5: Check set \(\{12,20,32\}\)

Here \(a = 12\), \(b=20\), \(c = 32\). Calculate \(a + b=12+20 = 32\). Since \(32=32\) (not greater than).

Answer:

\(\{8,15,21\}\)