Question

which of the following sets of numbers could not represent the three sides of a triangle?
answer
{9,23,31} {11,15,28}
{14,22,34} {12,16,26}

Explanation:

Step1: Recall triangle inequality rule

For three side lengths $a, b, c$ (where $c$ is the largest), $a + b > c$ must hold.

Step2: Test set {9,23,31}

Largest side is 31. Calculate sum of smaller sides: $9 + 23 = 32$. $32 > 31$, so valid.

Step3: Test set {14,22,34}

Largest side is 34. Calculate sum of smaller sides: $14 + 22 = 36$. $36 > 34$, so valid.

Step4: Test set {11,15,28}

Largest side is 28. Calculate sum of smaller sides: $11 + 15 = 26$. $26 < 28$, so invalid.

Step5: Test set {12,16,26}

Largest side is 26. Calculate sum of smaller sides: $12 + 16 = 28$. $28 > 26$, so valid.

Answer:

{11, 15, 28}