an acute triangle will have the longest side shorter than the hypotenuse of a right triangle
a right triangle would have sides in a ratio of 8-12 - sqr(64+144) or sqr208 =2x
x< (1/2)sqr208 makes the triangle acute
x< about 7.21
but x also has to be large enough so that 12^2 < 8^2 + (2x)^2
144 < 64 + 4x^2
4x^2 > 144-64 = 80
x^2 > 80/4 = 20
x > sqr20 = 2sqr5 = about 4.47
4.47 < x < 7.21
x = 5, 6 or 7 would make the triangle acute
but it's not the longest side if x=5 or 6
so x = 7 is the only integer solution and
6<x< about 7.21
x=3, 4 or 8 or 9 would make it obtuse
just to have a triangle, of any type, the longest side can't be > sum of the other sides
2x < 8+12
x < 10
and any side can't be less than the difference of the other two sides
2x>12-8 =4
2x>4
x > 2
2<x<10
