Answer:
[tex]{ \tt{L = 4\pi zt + 5\pi {z}^{2} }} \\ \\ { \tt{L = \pi z(4t + 5z)}} \\ \\ { \tt{ \frac{L}{\pi z} = 4t + 5z}} \\ \\ { \tt{4t = \frac{L}{\pi z} - 5z}} \\ \\ { \tt{t = \frac{L}{4\pi z} - \frac{5z}{4} }} \\ \\ { \boxed{ \tt{t = \frac{L - 5\pi {z}^{2} }{4\pi z} }}}[/tex]
