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 person showing cause, as aforesaid, why the prayer of said petition should not be granted. The failure of any person interested in said district or consolidated district to show cause, in writing, why the tract or tracts of land mentioned in said petition should not be excluded from said district, or the former district mentioned should not be excluded from the consolidated district, as the case may be, shall be deemed and taken as an assent by him or her to such exclusion, and the filing of such petition with such board, as aforesaid, shall be deemed and taken as an assent by each and all of such petitioners to such exclusion.