Question

which of the following sets of numbers could represent the three sides of a triangle?
answer
{11, 18, 30}
{5, 10, 16}
{10, 22, 34}
{6, 8, 12}

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 set \(\{11,18,30\}\)

\(11 + 18=29<30\), so it cannot form a triangle

Step3: Check set \(\{5,10,16\}\)

\(5+10 = 15<16\), so it cannot form a triangle

Step4: Check set \(\{10,22,34\}\)

\(10 + 22=32<34\), so it cannot form a triangle

Step5: Check set \(\{6,8,12\}\)

\(6+8 = 14>12\), \(6 + 12=18>8\), \(8+12 = 20>6\)

Answer:

\(\{6,8,12\}\)