(a) This section applies only to a county that has:
(1) a population of 90,001 to 225,000;
(2) an assessed valuation on property for property tax purposes of more than $125 million;
(3) four or more municipalities; and
(4) a municipality with a population of more than 50,000.
(b) If the commissioners court of a county determines that the courthouse is inadequate to properly house all county offices, that the jail is inadequate to properly confine prisoners, or that an agricultural building is necessary, the commissioners court may purchase, construct, or acquire in another manner a building and, when necessary, a site for the building to satisfy the determined need at any location in the county. The building may contain an auditorium, which may be used by the commissioners court or a county office or officer for any proper county or public purpose. The building or site must be paid for from the permanent improvement fund.