Question

question
which of the following sets of numbers could not represent the three sides of a triangle?
answer
{5,12,15} {5,10,13}
{14,27,40} {10,12,24}

Explanation:

Step1: Recall Triangle Inequality

For three sides \(a\), \(b\), \(c\) (where \(c\) is the largest), the triangle inequality states \(a + b>c\).

Step2: Check \(\{5, 12, 15\}\)

Largest side: \(15\). \(5 + 12=17>15\). Valid.

Step3: Check \(\{5, 10, 13\}\)

Largest side: \(13\). \(5 + 10 = 15>13\). Valid.

Step4: Check \(\{14, 27, 40\}\)

Largest side: \(40\). \(14+27 = 41>40\). Valid.

Step5: Check \(\{10, 12, 24\}\)

Largest side: \(24\). \(10 + 12=22<24\). Not valid.

Answer:

\(\{10, 12, 24\}\)