I need help with a problem I found in a book called "Geometrical Puzzles". I need to determine what fractal of the area of the outer square the area of the inner square is. (See the image)
Now, I do know it's in fact 1/5, but I also need to prove that. That's what I got so far: (a is the len of the outer square)
DQ² = a² + 1/2a²; DQ = √(1,5a²)
gQ = 1/5 * √(1,5a²)
hg = 2/5 * √(1,5a²)
It's no problem showing that Dh=hg=2*gQ=gf=ef=eh...using the intercept theorem.
But now, when I want to calculate the area of hg², I get instead of 1/5a² (=0,25a²) only 0,24a². That's a close miss....What the hell am I doing wrong?