An axial load P is supported by a short W250 x 67 column of cross-sectional area A=8580 mm^2 and is distributed to a concret foundation by a square plate as shown . knowing that the average normal stress in the column must not exceed 150 MPa and that the bearing stress on the concrete foundaton must not exceed 12.5 MPa , determine the side (a) of the plate that will provide the most economical and safe design .