[tex]\it \dfrac{DM}{MF}=\dfrac{9}{16} \Rightarrow DM=9k,\ \ MF=16k,\ \ k\in\mathbb{R_{+}^*}\\ \\ DF =DM+MF=9k+16k=25k\ \ \ \ \ \ (1)\\ \\ DF=100\ \ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow 25k=100|_{:25} \Rightarrow k=4 \Rightarrow DM=36\ cm,\ \ MF=64\ cm\\ \\ T.h. \Rightarrow EM^2=DM\cdot MF=36\cdot64=6^2\cdot8^2 \Rightarrow EM=6\cdot8=48\ cm[/tex]
