If a majority of the acreage represented at such meeting shall vote in favor of such extension the board of supervisors shall, not less than ten days before the next term of the court of common pleas, file a petition with the clerk of such court, praying for the extension of the corporate existence of the district. After filing the petition the same proceedings shall be had as is provided for in this chapter relating to the incorporation of the district. If such petition be granted by the court within ten days thereafter the clerk shall transmit a copy of the decree to the secretary of the board of supervisors, a copy to the Secretary of State and a copy to the clerk of the court of common pleas of each county having land in the district. Such clerks shall file and preserve the copies in their respective offices and for such service shall each receive a fee of one dollar. In case the court should find that such extension should not be allowed the petition shall be dismissed and the cost incurred in the case be paid by the district.