Question

which of the following sets of numbers could not represent the three sides of a triangle? answer {10,23,33} {15,18,30} {4,11,13} {11,22,32}

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 {10, 23, 33}

$10 + 23=33$, but for a triangle $a + b>c$, here $10 + 23$ is not greater than $33$.

Step3: Check set {15, 18, 30}

$15+18 = 33>30$, $15 + 30=45>18$, $18+30 = 48>15$.

Step4: Check set {4, 11, 13}

$4+11 = 15>13$, $4 + 13=17>11$, $11+13 = 24>4$.

Step5: Check set {11, 22, 32}

$11+22 = 33>32$, $11 + 32=43>22$, $22+32 = 54>11$.

Answer:

{10, 23, 33}