Answer:
[tex]z=11[/tex]
Step-by-step explanation:
The perimeter of a rectangle is found using the formula;
[tex]p=2w+2l[/tex]
The width of the rectangle is [tex]w=3z+2[/tex].
The length of the rectangle is [tex]l=4z[/tex]
The perimeter of the rectangle is [tex]p=158[/tex]
We substitute the given values to obtain;
[tex]158=2(3z+2)+2(4z)[/tex]
Expand to obtain;
[tex]158=6z+4+8z[/tex]
Group similar terms to get;
[tex]158-4=6z+8z[/tex]
Simplify;
[tex]154=14z[/tex]
[tex]z=11[/tex]
