Question

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 lengths \(a\), \(b\), \(c\) to form a triangle, the sum of any two sides must be greater than the third side. So we check \(a + b>c\), \(a + c>b\), and \(b + c>a\) for each set.

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

• \(12 + 24 = 36\), and \(36<37\). So this set fails.

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

• \(12 + 24 = 36\), and \(36<38\). This set fails.

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

• \(8 + 15 = 23>21\)
• \(8 + 21 = 29>15\)
• \(15 + 21 = 36>8\). All inequalities hold.

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

• \(12 + 20 = 32\), and \(32 = 32\) (not greater). This set fails.

Answer:

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