When any such agreement has been entered of record by the county court as directed in §§ 14-299-201 and 14-299-202, then all the owners of land in the township or in the area affected, whether they have signed the statement and agreement or not, shall become liable to pay their proportionate part of the costs of the improvement to the same extent, in the same manner, and subject to the same procedure to collect the costs, as applies to the signers of the agreement.