If any person interested in the district, or the proposed change of its boundaries shall show cause as aforesaid why such boundaries should not be changed, and shall not withdraw the same, and if the board of directors deems it for the best interest of the district that the boundaries thereof be so changed as to include therein the lands mentioned in the petition, or some part thereof, the board shall adopt a resolution to that effect. The resolution shall describe the exterior boundaries of the lands which the board is of the opinion should be included within the boundaries of the district when changed.