Question

which of the following sets of numbers could not represent the three sides of a triangle? answer {6,16,19} {4,19,25} {14,18,30} {4,11,13}

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 $\{6,16,19\}$

$6 + 16=22>19$, $6+19 = 25>16$, $16 + 19=35>6$. So it can form a triangle.

Step3: Check set $\{4,19,25\}$

$4+19 = 23<25$. Since the sum of two sides ($4$ and $19$) is less than the third side ($25$), it cannot form a triangle.

Step4: Check set $\{14,18,30\}$

$14 + 18=32>30$, $14+30 = 44>18$, $18 + 30=48>14$. So it can form a triangle.

Step5: Check set $\{4,11,13\}$

$4+11 = 15>13$, $4 + 13=17>11$, $11+13 = 24>4$. So it can form a triangle.

Answer:

B. $\{4,19,25\}$