A rectangular footing is to be designed to support a column load of $400$ kN$.$ The allowable bearing capacity of the soil is $200$ kN$/$m$^2.$ The footing is placed at a depth of $1\mathrm{.}5$ meters below the ground surface. Calculate the required dimensions of the footing if the factor of safety against bearing capacity failure is taken as $3.$ Assume the weight of the footing is negligible.

Step $1$: Calculate the area required for the footing.

Step $2$: Determine the dimensions of the footing.