Question

Which of the following sets of numbers could represent the three sides of a triangle? O {6, 18, 24} O {5,16,22} Submit Answer O {11, 17,27} O {8, 15, 24}

Answer 1

Given:

The objective is to find the numbers representing the three sides of a triangle.

The general condition for three sides of a triangles is,

`\text{Longest side< Sum of the other two sides}`

In option (a),

`\begin{gathered} 24=18+6 \\ 24=24 \end{gathered}`

Thus, option (a) cannot form a triangle.

Now, in option (b),

`\begin{gathered} 22>16+5 \\ 22>21 \end{gathered}`

Thus, option (b) cannot form a triangle.

Now, in option (c),

`\begin{gathered} 27<11+27 \\ 27<38 \end{gathered}`

Thus, option (c) can form a triangle.

Now, in option (d),

`\begin{gathered} 24>15+8 \\ 24>23 \end{gathered}`

Thus, option (d) cannot form a triangle.

Hence, option (c) is the correct anwer.