Any one or more freeholders owning more than fifty percent of the acreage desired to be included within the proposed weed district may file a petition with the board of county commissioners praying that their land be included, either separately or with other lands included in the petition, in a weed district to be formed for the purpose of destroying, preventing or exterminating any one or all such weeds, or that such lands be included within a district already formed, or a new district or districts to be formed out of any district or districts then existing. Such petition shall state the boundaries of the proposed district, the approximate number of acres in the proposed district, the particular weed or weeds to be destroyed, prevented or exterminated, the general method or means to be used in such work, and shall contain a list of all known land owners within the proposed district, together with the addresses of such land owners. Upon the filing of such petition the board of county commissioners shall fix a time for a hearing thereon, and shall give at least thirty days' notice of the time and place of such hearing by posting copies of such notice in three conspicuous places within the proposed district, one copy of which shall be at the main entrance to the courthouse, and by mailing a copy of such notice to each of the land owners named in the petition at the address therein named, and if any of the land described in the petition be owned by the state, a copy thereof shall be mailed to the department of natural resources at Olympia.