that will break down into 4 or 5 pieces which is the typical way. More than likely when broken down it should fit. You may have to share with another part of the car if worse comes to worse with fitting all the pieces. Usually the base is the longest biggest piece. As a rough you are dealing with the base being over 40 inches long and over 20 inches wide, but some are bigger.
There are a few scooters out there that completely fold down as one piece, but I doubt those are available for renting too much. Ask care Medical about your scooter and it's dimensions. Then ask the same about the car's trunk. You should get a good idea that way.