Upon such petition the court may appoint three (3) commissioners to make a survey of the land within and adjacent to the harbor line, covering the area of land as the commissioners may deem necessary, to include the interests of all persons whose rights may be affected by the determination of the lines; and the commissioners, being first sworn to a faithful discharge of their duties, shall determine the boundary lines of the interests of all the persons whose rights may be affected by the determination of the lines, and shall report to the court the boundaries so established, with a plat of the land, within and adjacent to the harbor line, showing the lines established for each person having an interest therein, which plat, after its approval by the court, shall by order of the court be recorded in the records of land evidence in the town where such land lies and in the office of the director of environmental management.