$\begin{align}  & EF\left\| BC \right.\Rightarrow \frac{AE}{AB}=\frac{EF}{BC}\Rightarrow \frac{2}{8}=\frac{EF}{20}\Rightarrow EF=5 \\  & MN\left\| BC \right.\Rightarrow \frac{AM}{AB}=\frac{MN}{BC}\Rightarrow \frac{3}{8}=\frac{MN}{20}\Rightarrow MN=\frac{15}{2} \\  & PQ\left\| BC \right.\Rightarrow \frac{AP}{AB}=\frac{PQ}{BC}\Rightarrow \frac{7}{8}=\frac{PQ}{20}\Rightarrow PQ=\frac{35}{2} \\  & EF+MN+PQ=5+\frac{15}{2}+\frac{35}{2}=30 \\ \end{align}$