When the board of county commissioners shall have finally determined and fixed the route and plans for the proposed system of improvement and the boundaries of the improvement district, and when it shall appear that the damages for property to be taken or damaged have been settled in the manner hereinabove provided, or when it shall appear that such damages have been settled as to a particular portion of the proposed improvement, and that construction of such portion of such proposed improvement is feasible, thereupon such system of improvement or such portion thereof, as the case may be, shall be constructed in the manner hereinafter provided.