Perimeter simply means the sum of all sides of the triangle
The given sides are:
[tex]4z,z+1,5z-1[/tex]
We will sum the sides as follow
[tex]\begin{gathered} 4z+z+1+5z-1 \\ \text{collecting like terms} \\ 4z+z+5z+1-1 \\ 10z \end{gathered}[/tex]
We will now equate the value obtained to the given perimeter (60)
[tex]\begin{gathered} 10z=60 \\ z=\frac{60}{10} \\ z=6 \end{gathered}[/tex]
The value of z = 6
