Solution #1: side lengths of the triangle x-1, x, x+1. A = 4 * (3x)/2 = 6x A = (x^3 -x)/4R A = \sqrt{3x/2(x/2+ 1)(x/2)(x/2 - 1)} 24xR = x(x^2 - 1) 24R = x^2 -1 R = (x+1)(x-1)/24 36x^2 = (3x/2)(x/2)(x^2/4 - 1) 36x^2 = 3x^4/16 - 3x^2/4 36 = 3x^2/16 - 3/4 147 * 4/3 = x^2 49 * 4 = x^2 14 = x. R = (14-1)(14+1)/24 = 13*15/24 = 13*5/8 = 65/8. Solution 2: 13,14,15 is a popular option to try first. It satisfies all conditions. So then the answer is just 65/8