Given:
Perimeter = 57 units
Side lengths:
3z
11
2z+3
z+1
12
We must remember that the perimeter is the sum of the distance of all the lengths of the sides.
To dertermine the value of z, we add the total lengths of the sides. So,
[tex]\begin{gathered} 3z+11+(2z+3)+(z+1_{})+12=57 \\ \end{gathered}[/tex]
Next, we combine like terms:
[tex]\begin{gathered} 3z+2z+z+11+3+1+12=57 \\ \text{Simplify and rearrange} \\ 6z+27=57 \\ 6z=57-27 \\ 6z=30 \\ z=\frac{30}{6} \\ \text{Calculate} \\ z=5 \end{gathered}[/tex]
Therefore, the value of z is 5.
