Question

which of the following sets of numbers could not represent the three sides of a triangle? answer {4,16,20} {11,13,23} {8,10,16} {8,11,17}

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 {4, 16, 20}

$4 + 16=20$, but for a triangle $a + b>c$. Here $4 + 16$ is not greater than $20$, so this set cannot be the sides of a triangle.

Step3: Check set {11, 13, 23}

$11+13 = 24>23$, $11 + 23=34>13$, $13+23 = 36>11$. This set can be the sides of a triangle.

Step4: Check set {8, 10, 16}

$8 + 10=18>16$, $8+16 = 24>10$, $10 + 16=26>8$. This set can be the sides of a triangle.

Step5: Check set {8, 11, 17}

$8+11 = 19>17$, $8 + 17=25>11$, $11+17 = 28>8$. This set can be the sides of a triangle.

Answer:

{4, 16, 20}