The board of directors at the time and place mentioned in the notice, or at the time or times to which the hearing of said petition may be adjourned, shall proceed to hear the petition and all objections thereto, presented in writing by any persons, showing cause as aforesaid why the prayer of said petition should not be granted. The filing of such petition with the board, as aforesaid, shall be deemed and taken as an assent by each and all of such petitioners to the exclusion from such district of the lands mentioned in the petition, or any part thereof.