If written protest is not made by the owners of one-half of the value of the territory proposed to be annexed, and if, at the conclusion of the hearing, the board finds and determines from the evidence presented at the hearing that the area proposed to be annexed to an improvement district will be benefited thereby, and that the improvement district to which the area proposed to be annexed will also be benefited thereby and will not be injured thereby, the board may, by resolution, approve such annexation.

The resolution shall describe the territory annexed, which may be by reference to a map on file with the secretary, which map shall govern for all details as to the extent of the annexed area. The resolution shall also state the terms and conditions of annexation as theretofore determined by resolution of the board.