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Firstly, I'd like to apologize for it taking me so long to reply to your query. I meant to respond earlier, had gotten caught up in something and had gotten distracted. Anyways, as for you question, well...it's not quite as simple as that in terms of dimensions (i.e Will it fit?). Each third party partner/manufacturer of Radeon products have varying differences to their designs, from different sized pcb's, heatsink/cooling units, fan quantity, casing materials and multiple other facets of their respective completed product.
So, with that being said each are usually slightly different. Here below I have presented a helpful dimensions tree for each of the third party manufacturer's R9 290's via Toms Hardware. To determine whether or not a specific R9 290 (will or will not) be compatible with your case size, simply check the document below as reference.
Now as for the other question, "Would I need to buy a different motherboard?". That remains to be seen. The answer is likely no, but without knowing your motherboard details, I can't specifically determine a correct response. With that being said, please list your complete computer specifications in the following format found via this location ( https://community.amd.com/thread/196209 ).
This will allow myself or another community technician a deeper insight in regards to your rig. This will eliminate any possible headaches down the line for you in the case that there are any other components that may need to be upgraded prior to an R9 290 (or higher) purchase. It's always better off to definitively know your upgrade path is on the right track, leaving no question unanswered.
One of the experienced community technicians will respond as soon as you provide the requested details as noted above. If you'd like me to assist you personally, please leave me a personal message, letting me know that you've replied here with the requested data. It will help bring it to my attention and I'll respond as soon as possible.
Thank you for your patience and welcome to the AMD forums, have a nice day.