Question

Which of the following sets of numbers could represent the three sides of a triangle?O {11, 21, 33}O {14, 27, 43}Submit AnswerO {11, 13, 23}O {5, 8, 15}

Answer 1

A triangle of sides a, b, c must follow the rules:

`\begin{gathered} a+b>c \\ b+c>a \\ a+c>b \end{gathered}`

Let's check the given options:

a. {11, 21, 33}:

`\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}`

b. {14,27,43}:

`\begin{gathered} 14+27>43 \\ 41>43 \\ \text{This is false, then this is not a triangle} \end{gathered}`

c. {11,13,23}:

`\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}`

d. {5,8,15}:

`\begin{gathered} 5+8>15 \\ 13>15 \\ \text{This is false, then this is not a triangle} \end{gathered}`

Answer: the set of numbers that could represent the three sides of a triangle is the third-one { 11, 13, 23 }