When a majority of the lot owners on any street in any block within the platted limits of an unincorporated townsite shall petition the board of supervisors of the township in which the unincorporated townsite, or the greater portion thereof, is situated, praying that a sidewalk be constructed or streetlights be installed along the side of a street or thoroughfare within the platted limits described in the petition, the board, by resolution, shall order the construction of the sidewalk or a portion thereof by the owner of the land along which the sidewalk is to be built, if it appears that the sidewalk described and prayed for in the petition is necessary to connect sidewalks already built or that public convenience and necessity require its construction, and shall order and make all necessary contracts and arrangements for the installation of streetlights if the public convenience or necessity require the installation.