Eagle CAD license board limitation: area or edges?
If you want to make a 200mm by 50mm board, you will run into placement problems past 160mm. 
There are three ways to work around this.

1) You can work around this using a special placement function, but that can be tedious. It also will fail ERC most of the time. (From what I last remember when I tried this back in 5.X)

2) You can buy the Pro license. (My least favorite option personally)

3) You can use a different CAD program. (If you're a hobbyist, then look at KiCad. There are limitations, but board size isn't one.)

In the end, they're your only real options. However, please take it with a grain of salt as my EagleCAD experience stopped past 5.X