Upon acceptance of a plan, the officials of the merged area acting as a committee of the whole shall appoint a board of hospital trustees. The board of trustees shall then meet, elect a chairperson and adopt such rules for the organization of the board as may be necessary. The number and composition of the board shall be determined by the committee appointing the board; but as a matter of public policy the committee is directed to apportion the board into area districts in such a way that the residents of all of the merged area will be represented as nearly equally as possible on the board.