Recall that the perimeter of a rhombus is given by the following formula:
[tex]P=4s,[/tex]
where s is the side length.
Now, we are given that:
[tex]\begin{gathered} s=3x-4, \\ P=8. \end{gathered}[/tex]
Therefore:
[tex]8=4(3x-4)\text{.}[/tex]
Simplifying the above equation, we get:
[tex]8=12x-16.[/tex]
Adding 16 on both sides of the equation, we get:
[tex]\begin{gathered} 8+16=12x-16+16, \\ 24=12x\text{.} \end{gathered}[/tex]
Finally, dividing by 12, we get:
[tex]x=\frac{24}{12}=2.[/tex]
Answer:
[tex]x=2.[/tex]
