It could well be that your laptop was advertized as "720p capable", meaning that it is higher resolution than native 720p.
Sorry about misleading you earlier, I was looking at 1280x768 on the chart instead of 1366x768. 1366x768 is in fact 16:9, so it should be the right form factor.
That said, you also need to make sure the screen you are buying has the right mounting points, and uses the right video connector for your laptop. Every time I have bought a replacement screen for a laptop, the company selling it clearly lists what makes and models the screen is compatible with. If your model is listed, then you should not have a problem. If it does not work, then you contact them for a return/replacement... not normally a big deal.