[tex]\it \mathcal{P}_{AMP}=AM+MP+AP=24\ cm\ \ \ \ \ (1)\\ \\ \left.\begin{aligned} \it \mathcal{P}_{MNP}=MN+NP+MP=32\ cm\\ \\ MN=MP\\ \\ AN=AP \Rightarrow NP=2AP\end{aligned}\right\} \Rightarrow MP+2AP+MP=32 \Rightarrow \\ \\ \\ \Rightarrow 2MP+2AP=32|_{:2} \Rightarrow MP+AP=16\ \ \ \ \ (2)[/tex]
[tex]\it (1),\ (2) \Rightarrow AM+16=24|_{-16} \Rightarrow AM=8\ cm[/tex]
