Triplex zoned as single family

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Hi guys! I've kinda been playing the background here for a while. You guys offer up great advice. I need some help on a situation I'm in. I recently just purchased a triplex that is zoned as a single family dwelling. Before I purchased the property the prior owners were in the process of applying for a multifamily variance to zoning. I was anticipating it being approved by closing. As it stands the application hasn't been approved and I'm concerned this could be a serious issue. I've already listed the apartments for rent and have been getting a ton of inquiries, however I'm afraid to rent the units while the property is still zoned as a single family dwelling. Any advice or information on how I should move forward is appreciated.