If any person interested in said 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 deem it for the best interests 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 are of the opinion should be included within the boundaries of the district when changed.