Question

answer
which of the following sets of numbers could represent the three sides of a triangle?
{10, 16, 24}
{15, 28, 45}
{11, 24, 37}
{5, 15, 20}
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Explanation:

Step1: Recall triangle inequality theorem

For three side lengths \(a\), \(b\), \(c\) (\(a\leq b\leq c\)), the sum of the two shorter sides \(a + b>c\)

Step2: Check \(\{10,16,24\}\)

\(10 + 16=26>24\)

Step3: Check \(\{15,28,45\}\)

\(15 + 28 = 43<45\)

Step4: Check \(\{11,24,37\}\)

\(11+24 = 35<37\)

Step5: Check \(\{5,15,20\}\)

\(5+15=20\) (not greater than \(20\))

Answer:

\(\{10,16,24\}\)