Aspect ratio of a triangle of a meshed surface

Question

I need to calculate the aspect ratio of a triangle. I have the 3 points, and therefore I have the lengths and midpoints. I was attempting to use this tutorial (although its not much of one in my opinion), but it is very vague and doesn't give much information. Could someone elaborate, specifically on the rectangle creation part, or even share a bit of c++ code to solve this problem?

To James's solution:

double s = (a + b + c) / 2.0;
double AR = (a * b * c) / (8.0 * (s - a) * (s - b) * (s - c));

@James:

Cubit reports the following:

Function Name  Average      Std Dev      Minimum     Maximum
-------------  ---------    ---------    ---------   ---------
Aspect Ratio   1.000e+00    7.371e-04    1.000e+00   1.010e+00
--------------------------------------------------------------

Your formula reports the following:

Function Name  Average    Minimum    Maximum
-------------  ---------  --------   -------
Aspect Ratio   1.00006    1.000000   1.00972
--------------------------------------------

Answer 1

These are the definitions of aspect ratio for triangles I know:

Aspect ratio of a triangle is the ratio of the longest edge to shortest edge (so equilateral triangle has aspect ratio 1).

Aspect ratio of a triangle is the ratio of the circumradius to twice its inradius, so AR = abc/(8(s-a)(s-b)(s-c)) where a,b,c are the lengths of sides of the triangle and s = (a+b+c)/2. So, if a=b=c, then the aspect ratio is 1.

These are much easier to calculate than what you've given.