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I can't understand how "" has been replaced by a smiley
I tried to calculate the side of an equilateral triangle inscribed in a square in the general case. I refer to your figure, assume BD=a, BG=d, BH=x and DI=y. Pythagore theorem applied to GH, GI and HI as hypothenuses gives the two equations :
Thank you again for the help
Hope that helps,
(I tried posting a link to a picture but it wouldn't let me. For the most part its an equilateral triangle in a square. the triangle is slanted and is as large as possible. If you type equilateral triangle in a square into google search, its the first website and halfway down the website is the triangle/square picture.