I do not recall ever seeing a pairing of Audio Research amplification with Legacy Audio speakers. So, you may not get any response from users having such a rig.
Regarding the Whisper, you can read my recent article on the Whisper DSW on Dagogo.com. I have used Pathos, Jeff Rowland's Class D amps, Cambridge Audio, Moscode (and a couple brands under review) with them. If you have an interest in any of these amps feel free to email me.
Your room will not be a problem; my room is similar dimensions. The Audio Research VS115 is a bit underpowered for my tastes. I have used as little as 70wpc of the Pathos Classic One MkIII and as much as 1,000wpc of the Jeff Rowland 606 Multi-channel. The AR amp will work with the Whisper. You can make nearly any stereo amp work since it has an active crossover you can adjust the gain to match amps, and the speaker has higher sensitivity of 95dB into 4 Ohms.
There is, however, a pronounced difference in dynamics and soundstage which is attainable with a more powerful amp regardless of brand. The benefit of a more powerful amp, all other things equal, is heard throughout the frequency spectrum, not just on the low end. Your best results would be to have an amp on the mid/top with at least 200-300wpc.
A more powerful Audio Research might be fantastic sounding, and though I have not tried it I likely could get very good sound with that manufacturer's products. The good thing about this situation is that if you must stay with a more modestly powered amp, the internal 500wpc bass amp in the speaker will give you very clean low end. So, it's not a matter of poor vs. good performance, but of good vs. superb performance. :)
One last thought; I normally encourage systems to be built using one brand of cables until tweaking the sound at the end. I normally try to stay with one brand and not mix cables. Once in a while I will add a power cord or two, or one set of interconnects, or a different digital cable. But I do not slap together a bunch of different brands.
In the case of the Whisper having a different amp (possibly with different technology as well) inside you will want to find your best brand of cable, then try different models of interconnect or speaker cables from that line to find the perfect balance between the bass and mid/treble. If necessary, try mixing brands slightly to find a better result. I only recommend this as an aid to helping in case your selected amp for Mid/High does not match perfectly to your ear with the bass.
When you find the perfect match for an amp to use with the Whisper I believe you will have an easier time using only one brand of cables on the entire system. I would still try some experimenting on cables, however, because of the hybrid nature of the speakers. With diligence you should be able to attain even better sound than a traditional dynamic speaker.
It seems you are in Bangladesh and perhaps the closest AR dealer is in India. You will want to check into reliability of any amp you consider as any repairs/shipping could be costly. It looks like a lot of water near you, so perhaps you could consider a solid state amp if you do not have air conditioning or if you are near the Bay of Bengal. I'm not an authority on this point, but I'm thinking the climate there might be harsh on tubed gear, shorten tube life, etc. You will want to communicate with the amp manufacturer to seek answers about it.
Regarding the Whisper, you can read my recent article on the Whisper DSW on Dagogo.com. I have used Pathos, Jeff Rowland's Class D amps, Cambridge Audio, Moscode (and a couple brands under review) with them. If you have an interest in any of these amps feel free to email me.
Your room will not be a problem; my room is similar dimensions. The Audio Research VS115 is a bit underpowered for my tastes. I have used as little as 70wpc of the Pathos Classic One MkIII and as much as 1,000wpc of the Jeff Rowland 606 Multi-channel. The AR amp will work with the Whisper. You can make nearly any stereo amp work since it has an active crossover you can adjust the gain to match amps, and the speaker has higher sensitivity of 95dB into 4 Ohms.
There is, however, a pronounced difference in dynamics and soundstage which is attainable with a more powerful amp regardless of brand. The benefit of a more powerful amp, all other things equal, is heard throughout the frequency spectrum, not just on the low end. Your best results would be to have an amp on the mid/top with at least 200-300wpc.
A more powerful Audio Research might be fantastic sounding, and though I have not tried it I likely could get very good sound with that manufacturer's products. The good thing about this situation is that if you must stay with a more modestly powered amp, the internal 500wpc bass amp in the speaker will give you very clean low end. So, it's not a matter of poor vs. good performance, but of good vs. superb performance. :)
One last thought; I normally encourage systems to be built using one brand of cables until tweaking the sound at the end. I normally try to stay with one brand and not mix cables. Once in a while I will add a power cord or two, or one set of interconnects, or a different digital cable. But I do not slap together a bunch of different brands.
In the case of the Whisper having a different amp (possibly with different technology as well) inside you will want to find your best brand of cable, then try different models of interconnect or speaker cables from that line to find the perfect balance between the bass and mid/treble. If necessary, try mixing brands slightly to find a better result. I only recommend this as an aid to helping in case your selected amp for Mid/High does not match perfectly to your ear with the bass.
When you find the perfect match for an amp to use with the Whisper I believe you will have an easier time using only one brand of cables on the entire system. I would still try some experimenting on cables, however, because of the hybrid nature of the speakers. With diligence you should be able to attain even better sound than a traditional dynamic speaker.
It seems you are in Bangladesh and perhaps the closest AR dealer is in India. You will want to check into reliability of any amp you consider as any repairs/shipping could be costly. It looks like a lot of water near you, so perhaps you could consider a solid state amp if you do not have air conditioning or if you are near the Bay of Bengal. I'm not an authority on this point, but I'm thinking the climate there might be harsh on tubed gear, shorten tube life, etc. You will want to communicate with the amp manufacturer to seek answers about it.