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 \(a\), \(b\), \(c\) (where \(c\) is the largest), the theorem states \(a + b>c\).

Step2: Check \(\{12,24,37\}\)

Largest side \(c = 37\). \(12 + 24=36\). Since \(36<37\), not a triangle.

Step3: Check \(\{12,24,38\}\)

Largest side \(c = 38\). \(12 + 24 = 36\). Since \(36<38\), not a triangle.

Step4: Check \(\{8,15,21\}\)

Largest side \(c = 21\). \(8 + 15=23\). Since \(23>21\), satisfies the theorem.

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

Largest side \(c = 32\). \(12 + 20 = 32\). Since \(32 = 32\) (needs to be greater), not a triangle.

Answer:

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