The board of directors, at the time and place mentioned in said notice, or at such other time or times to which the hearing of said petition may be adjourned, shall proceed to hear the petition and all the objections thereto presented in writing by any person showing cause, as aforesaid, why said proposed change of the boundaries of the district should not be made. The failure by any person interested in said district, or in the matter of the proposed change of its boundaries, to show cause in writing, as aforesaid, shall be deemed and taken as an assent on his or her part to a change of the boundaries of the district as prayed for in said petition, or to such a change thereof as will include a part of said lands. And the filing of such petition with said board, as aforesaid, shall be deemed and taken as an assent on the part of each and all of such petitioners to such a change of said boundaries that they may include the whole or any portion of the lands described in said petition.