The value of z is z = 5
To solve this, we need to create an equation. the perimeter of a rectangle is:
[tex]P=2L+2l[/tex]
Where L is the lenght of the longer sides and l the lenght of the shorter sides.
Then we know by the picture that:
[tex]\begin{gathered} L=3z-2 \\ l=2z \end{gathered}[/tex]
Replacing this values and the fact that the perimeter is 46 on the equation for the perimeter:
[tex]P=2L+2l\Rightarrow46=2(3z-2)+2(2z)[/tex]
Now solve for z:
[tex]\begin{gathered} 46=2\cdot3z+2(-2)+4z \\ 46=6z+4z-4 \\ 46+4=10z \\ 50=10z \\ \frac{50}{10}=z \\ z=5 \end{gathered}[/tex]
