A lot with a minimum width of 60 feet and a minimum area of 7,800 square feet per family shall be provided for every building hereafter erected, altered or used in whole or in part as a dwelling, provided that in the case of a lot held in single and separate ownership at the effective date of this chapter having smaller dimensions, or having an area of less than 7,800 square feet, a dwelling may be built thereon as a variance when authorized by the Zoning Hearing Board.