A foundation must be built on a non$-$cohesive soil that has the following characteristics: soil density $=18\mathrm{.}0$ kN$/$m$3,$ saturated soil density $=19\mathrm{.}0$ kN$/$m$3,$ internal friction angle of $30\backslash$deg $,$ depth of planting $=1\mathrm{.}5$ m and depth of water table $=0\mathrm{.}8$ m

The gross allowable load with FS $=3$ is $700$ kN$.$ Determine the dimensions of the proposed footing using Meyerhof theory.