In case the report of the commissioners shall contain assessments of benefits and damages to lands not included in the original petition as signed and filed the board of supervisors shall file in the office of the clerk a petition praying that the court grant permission for the extension of the boundary lines of the district so as to embrace all lands that will be benefited, as shown by the report of the commissioners, and after such petition has been filed it shall be proceeded with in accordance with the provisions of this chapter governing the extension of boundary lines of districts.