The perimeter of a figure is the sum of lengths of the sides.
For the given rectangle the perimeter is:
[tex]\begin{gathered} P=2(3z-3)+2(2z) \\ \\ 74=2(3z-3)+2(2z) \end{gathered}[/tex]
Use the equation above to solve z:
[tex]\begin{gathered} 74=6z-6+4z \\ 74=10z-6 \\ 74+6=10z-6+6 \\ 80=10z \\ \frac{80}{10}=\frac{10z}{10} \\ \\ 8=z \\ \\ z=8 \end{gathered}[/tex]
Use the vlue of z to find the length of AD:
[tex]\begin{gathered} AD=3z-3 \\ AD=3(8)-3 \\ AD=24-3 \\ AD=21 \end{gathered}[/tex]
Then, the length of side AD is 21 units
