[tex]\displaystyle\bf\\L_d=45~cm\\\\l_d=\frac{7}{9}\times L_d=\frac{7}{9}\times 45=7\times5=35~cm\\\\P_d=2(45+35)=2\times80=160~cm\\\\P_p=\frac{2}{5}\times~P_d=\frac{2}{5}\times~160=2\times32=64~cm\\\\Lp=\frac{P_p}{4}=\frac{64}{4}=16~cm\\\\ \boxed{\bf Lp=16~cm}[/tex]