Section 112. The appellant, to perfect the appeal, shall, within twenty days after filing the notice thereof, file with the clerk of the department a petition stating the reasons for the appeal, and shall, within ten days after filing the petition, cause a certified copy thereof to be served upon the county commissioners. An appeal may be waived at any time before a hearing thereon by written agreement of the parties, filed with the county commissioners and the department. If the appellant fails to perfect the appeal, or if the appeal is waived, the matter may proceed before the county commissioners as if no appeal had been taken.