Two strings $\mathrm{A}$ and $\mathrm{B}$ of lengths, $L_A=80\mathrm{ }\mathrm{cm}$ and $L_B=x\mathrm{ }\mathrm{cm}$ respectively are used separately in a sonometer. The ratio of their densities is $0.81$. the diameter of $\mathrm{B}$ is one-half that of $\mathrm{A}$. if the strings have the same tension and fundamental frequency the value of $x$ is