Two strings A and B of length, ${\mathrm{L}}_{\mathrm{A}}=80 \mathrm{cm} \text{and }{\mathrm{L}}_{\mathrm{B}}=\mathrm{x} \mathrm{cm}$ respectively are using separately in a string experiment. The ratio of their densities $\left(\frac{d_A}{d_B}\right)$  is 0.81. The diameter of B is one half that of A. If the strings have the same tension and same fundamental frequency then the value of x is