Question

which of the following sets of numbers could not represent the three sides of a triangle? answer {11,19,32} {11,23,31} {8,18,24} {7,22,27}

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step2: Check set {11, 19, 32}

$11 + 19=30<32$. This set does not satisfy the triangle - inequality theorem.

Step3: Check set {11, 23, 31}

$11+23 = 34>31$, $11 + 31=42>23$, $23+31 = 54>11$. It satisfies the theorem.

Step4: Check set {8, 18, 24}

$8 + 18=26>24$, $8+24 = 32>18$, $18 + 24=42>8$. It satisfies the theorem.

Step5: Check set {7, 22, 27}

$7+22 = 29>27$, $7 + 27=34>22$, $22+27 = 49>7$. It satisfies the theorem.

Answer:

{11, 19, 32}