Question

which of the following sets of numbers could not represent the three sides of a triangle?
answer
{7,10,15}
{5,15,20}
{6,15,19}
{4,12,15}
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Explanation:

Step1: Apply triangle inequality theorem

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

Step2: Check \(\{5,15,20\}\)

Here \(a = 5\), \(b=15\), \(c = 20\). Then \(a + b=5 + 15=20\), and \(20
ot>20\).

Step3: Check \(\{7,10,15\}\)

\(a = 7\), \(b = 10\), \(c=15\). \(a + b=7+10 = 17>15\).

Step4: Check \(\{4,12,15\}\)

\(a = 4\), \(b = 12\), \(c = 15\). \(a + b=4 + 12=16>15\).

Step5: Check \(\{6,15,19\}\)

\(a = 6\), \(b = 15\), \(c=19\). \(a + b=6+15 = 21>19\).

Answer:

\(\{5,15,20\}\)