A load test is performed on a $0\mathrm{.}3$m by $0\mathrm{.}3$m square plate on a dense cohesionless sand

$($unit weight $=18$ kN$/$m$3$

$).$ The plate$$s base is located $0\mathrm{.}6$ m below the ground surface. If the

plate fails at a load of $82$ kN$,$ what is the failure load per unit area of the base of a square

footing $2$m by $2$m loaded with its base at the same depth in the same materials? $($