Whenever the owners of more than 51% of the lineal frontage of lands outside of the corporate limits of any city or village fronting or touching upon any public highway or portion thereof, desire a pavement or sidewalks built thereon, they may file an application for such improvement with the county road commissioners of the county in which such pavement or sidewalk is proposed to be built. No application for the paving of any highway, or portion thereof, shall be considered unless at least 75% of the lands fronting thereon have been subdivided into parcels having a frontage of not more than 300 feet each on such highway or there shall be an average of at least 1 building, including buildings under construction, located along the portion of such highway proposed to be paved for every 300 lineal feet thereof, according to a survey thereof to be made by the commissioners. The eligibility of signers to any application hereby authorized may be determined by their interest of record in the office of the register of deeds or in the probate court of the county in which such lands are situated at the time the petition is presented or by other satisfactory proof of interest presented to the commissioners. Such petition shall be accompanied by a description of the land fronting or touching on the highway owned by each signer and by a certificate of the county treasurer, showing the taxes or special assessments, if any, against such lands which appear delinquent on his books; no name of any signer on the petition shall be considered valid whose land fronting or touching on the highways shows delinquent assessments or taxes on such certificate. Any petition so received by the commissioners or presented to them under the provisions of this act, shall be deemed to confer full authority to cause such work to be done in order that the proper proportion of the expense thereof may be met accordingly. The commissioners shall have all the power of laying out and establishing all such pavements or sidewalks. The words “highway” or “public highway” as used in this act mean any road, street or alley taken over by and under the jurisdiction of the board of county road commissioners.