The board of directors to whom such petition to include other lands in the district is presented, shall require, as a condition precedent to the granting of the petition, that the petitioners shall severally pay, or give approved security upon such terms as may be prescribed by the board to pay, to such district such respective sums as shall be determined by the board at the hearing above provided for, which sums shall be such equitable amount as such land shall pay having regard to placing said lands on the basis of equality with other lands in the district as to benefits received, and such lands shall also become subject to all taxes and assessments of the district thereafter imposed.