Question

question which of the following sets of numbers could not represent the three sides of a triangle? answer {15,17,31} {6,10,16} {8,16,23} {6,14,17} submit answer watch video show examples

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 each set

• For \(\{6,10,16\}\): \(6 + 10=16\), which does not satisfy \(a + b>c\) (since \(6+10

ot>16\)).

• For \(\{15,17,31\}\): \(15+17 = 32>31\), \(15 + 31>17\), \(17+31>15\).
• For \(\{6,14,17\}\): \(6+14 = 20>17\), \(6 + 17>14\), \(14+17>6\).
• For \(\{8,16,23\}\): \(8+16=24>23\), \(8 + 23>16\), \(16+23>8\).

Answer:

\(\{6,10,16\}\)