The state of Virginia sold $57 million in revenue bonds yesterday to pay for construction of the long-awaited 13-mile Dulles Toll Road, which will link rapidly growing western Fairfax County with downtown Washington and is expected to spur development along the virtually empty Dulles corridor.

"It's the last step in a long trail," said Fairfax County Board Chairman John F. Herrity, adding that the toll road, which is supposed to pay for itself by the year 2007, will alleviate "significant traffic jams" in the Tysons Corner area when it is completed in 1984.

Sale of the bonds at an interest rate of 9.1 percent was the final step before construction starts next month. The road will run parallel to the existing toll-free Dulles Airport Access Road and will provide connections to I-66 and the Capital Beltway at its eastern terminus. It is expected to serve 20,000 to 30,000 commuting trips a day. Those commuters who drive the entire route will pay 75 cents per car for a one-way trip.

Fairfax County has placed a high priority on development of the Dulles corridor, and Fairfax officials have anxiously shepherded the toll road since the state legislature approved it in 1979. When it seemed that high interest rates might drive costs over the state-approved $57 million, the Fairfax board was worried enough to award a noncompetitive $1.5 million contract to a local design firm to speed construction plans. The board also allocated an additional $5 million in construction money. "We were anxious to take advantage of the depressed construction market," Fairfax County Transportation Director Shiva K. Pant said yesterday.

Fairfax and Loudoun county commuters have complained for years about overcrowded local roads and the underused Dulles Access Road, which the Federal Aviation Administration restricts to airport traffic and a few commuter buses. The FAA, which owns the airport and access road, has resisted pressure to open the airport road to commuter traffic.

In addition, Herrity had said that failure to build the road and alleviate traffic congestion could jeopardize the 55 percent of the industrially zoned land between Tysons Corner and Dulles Airport.

Some transportation specialists have called the toll road an anachronism and criticized Fairfax County for pushing construction of such a road in an era when planners are trying to wean Americans from the private automobile. If toll revenues do not cover the Dulles Toll Road construction costs, the state, not Fairfax County, will pay the balance.

Although Herrity praised the bond sale, Supervisor Audrey Moore predicted the road will prove a "bonanza" for developers and said she is worried about the effect rapid development will have on county resources in the future.

The state-maintained toll road will include 10 interchanges plus special ramps to Wolf Trap Farm Park performing arts center. There will be a major toll facility between the Beltway and Rte. 7.

The FAA wrangled this summer with homeowners along the proposed road over the cost and number of noise barriers to be provided. The FAA decided recently to require about $5 million in barriers in five locations, including Wolf Trap Farm Park and some,but not all, of the subdivisions that had requested them.