A square foundation $($B$*$B$)$ rests on a soil that has a specific saturated weight of $160$ pounds$/$cubic foot, the level of foundation displacement is $5$ feet, and the water table is $3$ feet from the ground surface. The specific weight of the soil above the water table corresponds to $130$ pounds$/$cubic foot.

The gross allowable load falling on the foundation pedestal corresponds to $200,000$ pounds, calculated with a safety factor of four $(4).$

Determine the size of the foundation, using the method of the general load capacity equation $($Meyerhof method$).$