The board of directors, if they deem it not for the best interests of the district that a change of its boundaries be so made as to include therein the lands mentioned in the petition, shall order that the petition be rejected. But if they deem it for the best interests of the district that the boundaries of said district be changed, and if no person interested in said district, or the proposed change of its boundaries, shows cause in writing why the proposed change should not be made, or if, having shown cause, withdraws the same, the board may order that the boundaries of the district be so changed as to include therein the lands mentioned in said petition, or some part thereof. The order shall describe the boundaries of lands included, as aforesaid; and for that purpose the board may cause a survey to be made of such portions of such boundary as is deemed necessary and may at its option redefine the boundaries of the district, or so much of the same as it deems advisable.