Question

multiple choice 2 points 19 which set of numbers can not represent the lengths of the sides of a triangle? {9,12,19} {7,5,6} {6,8,11} {7,18,11}

Explanation:

Step1: Apply triangle inequality theorem

For three side lengths \(a\), \(b\), \(c\) (\(a\leq b\leq c\)), the triangle inequality theorem states that \(a + b>c\).

Step2: Check set \(\{7,5,6\}\)

Let \(a = 5\), \(b=6\), \(c = 7\). Then \(a + b=5 + 6=11>7\).

Step3: Check set \(\{6,8,11\}\)

Let \(a = 6\), \(b = 8\), \(c=11\). Then \(a + b=6 + 8 = 14>11\).

Step4: Check set \(\{7,18,11\}\)

Let \(a = 7\), \(b = 11\), \(c=18\). Then \(a + b=7+11 = 18\), and \(18
ot>18\) (violates \(a + b>c\)).

Step5: Check set \(\{9,12,19\}\)

Let \(a = 9\), \(b = 12\), \(c=19\). Then \(a + b=9 + 12=21>19\).

Answer:

\(\{7,18,11\}\)