Answer: [tex]PQ=16\ units[/tex]
Step-by-step explanation:
The missing figure is attached.
The perimeter of a rectangle is:
[tex]P=2l+2w[/tex]
Where "l" is the lenght and "w" is the width.
You can identify in the figure that:
[tex]w=SR=PQ=2z+2\\\\l=QR=PS=3z+1[/tex]
Then, knowing the perimeter of the rectangle, you can make the subsitution into the formula:
[tex]76=2(3z+1)+2(2z+2)[/tex]
Now you must simplify and solve for "z"
[tex]76=6z+2+4z+4\\\\76-6=10z\\\\70=10z\\\\\frac{70}{10}=z\\\\z=7[/tex]
Finally, substituting the value of "z" into [tex]PQ=2z+2[/tex], you get:
[tex]PQ=2(7)+2=16\ units[/tex]
