If, within sixty (60) days after the adoption and publication of the resolution by the governing board of the municipality, petitions are filed with the clerk or recorder of the municipality containing the signatures of a majority in value, number, and area of the real property to be located within the proposed district as shown by the last county assessment in the municipality, or the designated areas requesting that an improvement district be created for the purpose of making the improvements, then the clerk or recorder shall set a date and place for a public hearing on the sufficiency of the petitions.