The owners of land in a district may petition the drainage board to hold a district meeting. The petition shall be signed by at least 10 percent of the owners of land within the district or by the owners of at least 10 percent of the lands within the district. The drainage board shall either schedule a district meeting to be held within 60 days after receiving the petition or deny the petition, by issuing a published order, within 60 days after receiving the petition. The drainage board may deny the petition only on the grounds that it is unreasonable.