(1) The sanitary and improvement district may be enlarged and additional territory annexed to the district by either of the following methods:
(a) By petitions signed by the owner or owners of all the property to be annexed to the district. If such a petition requesting annexation is presented to the trustees and approved by the trustees the change in the boundaries to include the additional area shall be certified by the clerk of the district to the county clerk in which the greater portion of the district is located and thereafter the district shall include the area thus annexed.
(b) By a petition filed with the clerk of the district, signed by persons owning not less than fifty percent of the area to be annexed, but not signed by persons owning all the area requested to be annexed. On the filing of such petition, the trustees of the district shall fix a time and place for a hearing thereon and give notice of said hearing by two weekly publications and by either registered or certified mail to the record owners of all persons owning land within the territory sought to be annexed, not less than ten days prior to the date of said hearing, if the address of said owners is known or can be ascertained by reasonable diligence by the trustees. At the said meeting, any person owning property within the area proposed to be annexed or any person owning property or residing within the district may appear and be heard. If, after said hearing, the board of trustees find and determine that annexation of the additional area will be conducive to the public health, convenience, and welfare and will not be an undue burden on the district, the board of trustees may, by resolution, annex the additional area and fix the boundary thereof which shall not include more than the area requested in the petition. A copy of the said resolution shall be filed with the county clerk of the county in which the greater portion of the district is located and thereafter the area included by said resolution shall be a part of the district.
(2) All property, from and after it is annexed to the district as above provided, shall be subject to all taxes and other burdens thereafter levied by the district, regardless of when the obligation for which said taxes or assessments are levied was incurred.
(3) No lands included within any municipal corporation shall be included in any sanitary and improvement district, and no tract of twenty acres or more which is outside any municipal corporation and is used primarily for industrial purposes shall be included in any sanitary and improvement district organized under sections 31-727 to 31-762 without the written consent of the owner of such tract.