If the majority of the landowners owning one third of the acreage of the lands or one third of the landowners owning a majority in acreage of the lands proposed to be added to the existing drainage district shall petition the chancery court of any county in which any part of the land lies to extend the boundaries of the existing drainage district so as to embrace and include their lands, proceedings shall be held in all respects in conformity with the provisions of this chapter.