[tex]\displaystyle \\
l = \frac{1}{3}\times L \\ \\
P= 2L + 2l = 96~m \\ \\
2L + 2\times \frac{1}{3}\times L = 96 \\ \\
2L\Big(1 + \frac{1}{3}\Big) = 96 \\ \\
2L\times \frac{4}{3} = 96 \\ \\
\frac{8}{3}\times L = 96 \\ \\
L = 96 : \frac{8}{3} = 96 \times \frac{3}{8} =\frac{96\times 3}{8} = 12 \times 3 = \boxed{36 ~m} \\ \\
l = \frac{1}{3}\times L = \frac{L}{3} = \frac{36}{3} = \boxed{12 ~m}[/tex]
