A $0\mathrm{.}65mm$ Linear Low Density Polyethylene geomembrane with a mobilized allowable stress of $700l\frac{b}{i}{n}^2$ is installed on a $3(H)$:$1(V)$ side slope as shown in Figure $1.$ The cover soil above the geomembrane consists of two layers, a top layer of $6^{\text{'}\text{'}}$ in thickness with the unit weight $120l\frac{b}{f}{t}^3$ and a bottom layer of $6^{\text{'}\text{'}}$ in thickness with the unit weight $100l\frac{b}{f}{t}^3.$ The friction angle between the top layer soil and the bottom layer soil is $32.$ The friction angle between the geomembrane and the bottom layer soil is approximated as $25.$

a$)$ Determine the allowable force per meter width of the geomembrane.

b$)$ Determine the runout length $($state clearly the assumptions if any is used$).$