Question

which of the following sets of numbers could represent the three sides of a triangle?
answer
{11,26,38}
{15,17,34}
{6,14,18}
{15,23,40}
submit answer

Explanation:

Step1: Recall triangle inequality theorem

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

Step2: Test set {11,26,38}

Largest side is 38. $11 + 26 = 37$, and $37 < 38$. Fails the theorem.

Step3: Test set {15,17,34}

Largest side is 34. $15 + 17 = 32$, and $32 < 34$. Fails the theorem.

Step4: Test set {6,14,18}

Largest side is 18. $6 + 14 = 20$, and $20 > 18$. Also, $6 + 18 > 14$ and $14 + 18 > 6$. Passes the theorem.

Step5: Test set {15,23,40}

Largest side is 40. $15 + 23 = 38$, and $38 < 40$. Fails the theorem.

Answer:

{6, 14, 18}