Question

which of the following sets of numbers could represent the three sides of a triangle. 4,7,1212,16,284,12,137,13,22

Answer 1

4, 12, 13

Step-by-step explanation

The sum of any 2 sides of a triangle must be greater than the measure of the third side.

For these options we have to check which set of numbers follow this rule:

`\begin{gathered} 4+7>12 \\ 11>12\text{ }\rightarrow\text{ false} \end{gathered}`
`\begin{gathered} 12+16>28 \\ 28>28\text{ }\rightarrow\text{ false} \end{gathered}`
`\begin{gathered} 4+12>13 \\ 16>13\text{ }\rightarrow\text{ true} \\ 12+13>4 \\ 25>4\text{ }\rightarrow\text{ true} \\ 4+13>12 \\ 17>12\text{ }\rightarrow\text{ true} \end{gathered}`
`\begin{gathered} 7+13>22 \\ 20>22\rightarrow\text{ false} \end{gathered}`

The third set of numbers could represent the three sides of a triangle