I've tried and failed many times to come up with an equation to solve my sign size. i'm starting a sign business and i want signs of different ratios to look the "same" size. for instance, my 'medium' signs are from 22" to 29.5". if it's a perfect square or circle, it's 22 inches. but if the sign is, let's say, twice as wide as it is long, then it will be closer to 29.5. it's not based on square area per se. the following sign sizes are somewhat arbitrary, but when i put them in autocad, i'm ok with it. so a square would be 22" x 22", at a 1.4 ratio, the sign would be 26" x 17.6." at 7.35 ratio, the sign would be 29.5" x 4." 29.5 has to be the max.