Where any petition for the construction or improvement of any road or roads in a benefit district has been approved by the board of county commissioners and the construction or improvement of such road or roads for which no contract has been let within three years following the date of the approval on which no action has been taken other than filing such petitions such approval of the petition by the board of county commissioners shall be null, void and of no effect and such road or roads shall neither be constructed nor improved under such petition and approval.