According to the web page referenced above, the triangle should have sides with a length of 6.7664, which is different from the answer I got (6.4308). Assuming the web page is correct, could you please point out the flaw in my approach to the problem?

I figure that either one (or both) of my assumption, s+h=12 or h=sqrt(s2-s2/4), is incorrect, but I'm at a loss to see how. Any help you can offer would be much appreciated. Thank you.