The perimeter of a polygon is the sum of all its sides, therefore to find the length of the missing side we have to add the values for the three known ones and then subtract the result from the value of the perimeter. This is done below:
[tex]\begin{gathered} 7x+9+(10-2x)+(13x-15) \\ 7x+9+10-2x+13x-15 \\ 7x+13x-2x+9+10-15 \\ 18x+4 \end{gathered}[/tex]
Then we subtract this value from the perimeter:
[tex]\begin{gathered} 31x-12-(18x+4) \\ 31x-12-18x-4 \\ 31x-18x-12-4 \\ 13x-16 \end{gathered}[/tex]
The missing side has a length of 13x - 16.
