Respuesta :
A triangle of sides a, b, c must follow the rules:
[tex]\begin{gathered} a+b>c \\ b+c>a \\ a+c>b \end{gathered}[/tex]Let's check the given options:
a. {11, 21, 33}:
[tex]\begin{gathered} 11+21>33 \\ 33>33 \\ 33\text{ is not greater than 33, it is equal, then this is not a triangle} \end{gathered}[/tex]b. {14,27,43}:
[tex]\begin{gathered} 14+27>43 \\ 41>43 \\ \text{This is false, then this is not a triangle} \end{gathered}[/tex]c. {11,13,23}:
[tex]\begin{gathered} 11+13>23 \\ 24>23\text{ Ok} \\ 13+23>11 \\ 36>11\text{ OK} \\ 11+23>13 \\ 34>13\text{ Ok} \\ It\text{ follows the rules, then this is a triangle.} \end{gathered}[/tex]d. {5,8,15}:
[tex]\begin{gathered} 5+8>15 \\ 13>15 \\ \text{This is false, then this is not a triangle} \end{gathered}[/tex]Answer: the set of numbers that could represent the three sides of a triangle is the third-one { 11, 13, 23 }
