The most hydraulically efficient trapezoidal channel section to carry a discharge of $5$m$3/$s on a bed material with roughness n of $0\mathrm{.}02$ and a bottom slope of $1$ in $800$ should have a bottom width of$.$

a$.1\mathrm{.}65$m

b$.2\mathrm{.}65$m

c$.3\mathrm{.}65$m

d$.4\mathrm{.}65$m