Question

which of the following sets of numbers could not represent the three sides of a triangle? answer \\(\\{15,26,39\\}\\) \\(\\{8,10,15\\}\\) \\(\\{9,22,29\\}\\) \\(\\{8,17,27\\}\\)

Explanation:

Step1: Recall triangle inequality theorem

For sides $a,b,c$, sum of any two sides > third side. We only need to check if sum of two shorter sides > longest side.

Step2: Check set {15,26,39}

$\text{15 + 26 = 41}$, $41 > 39$, valid.

Step3: Check set {9,22,29}

$\text{9 + 22 = 31}$, $31 > 29$, valid.

Step4: Check set {8,10,15}

$\text{8 + 10 = 18}$, $18 > 15$, valid.

Step5: Check set {8,17,27}

$\text{8 + 17 = 25}$, $25 < 27$, invalid.

Answer:

{8,17,27}