Question

which of the following sets of numbers could represent the three sides of a triangle? answer {14,20,34} {9,20,28} {13,20,34} {11,14,27}

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 {14, 20, 34}

$14 + 20=34$, which does not satisfy the triangle - inequality theorem since $14 + 20$ is not greater than $34$.

Step3: Check set {9, 20, 28}

$9+20 = 29>28$, $9 + 28=37>20$, $20 + 28 = 48>9$. This set satisfies the triangle - inequality theorem.

Step4: Check set {13, 20, 34}

$13+20 = 33<34$, which does not satisfy the triangle - inequality theorem.

Step5: Check set {11, 14, 27}

$11 + 14=25<27$, which does not satisfy the triangle - inequality theorem.

Answer:

{9, 20, 28}