Graphics Card Size- Length?

Not all PCI slots are the same (lane count)

PCI-E 16's are used for GPUs and are the longest of them all. Most mother boards now a days have 1-3 of them.

Expansion Slots
2 x PCI
1 x PCI-e x 4
1 x PCI-e x 16
*taken from the website's listed specs
 
One thing you need to factor in is your machine has a 350watt factory power supply. That card requires a minimum 450watt PSU. The card requires a 6-pin PCIe supplementary power cable as well. While it may physically FIT in your case/ on your motherboard, you will likely have issues unless you upgrade your power supply as well