Will this r9 270x fit my case?

[Makkfej]

I have this pre-built computer: http://h20000.www2.hp.com/bizsupport/TechSupport/Document.jsp?objectID=c03062369&lang=en&cc=us&contentType=SupportFAQ&prodSeriesId=5151865&prodTypeId=12454
I want to know if this graphics card would fit in the case and on the motherboard: http://www.alza.sk/sapphire-r9-270x-vapor-x-oc-boost-d503893.htm
Dimensions are: 264x103x35 and it's a two-slot cooler.
Please don't suggest any other graphics card, just answer my question and explain why

 

[cin19]

Open the case, meaure the space like in the picture. http://www.hardwarecanucks.com/wp-content/uploads/lian-li-pc-case-3.jpg

 

[Makkfej]

Open the case, meaure the space like in the picture. http://www.hardwarecanucks.com/wp-content/uploads/lian-li-pc-case-3.jpg

I did that but i think that the ram will obstruct the graphics card because it's tight on the pci-e slot. I hope that it won't