Scroll down for a solution to this problem.
The fraction green : blue is 144/1369.
The whole problem is basically a comparison of scales. From similarity of triangles EGH and EBC we find HG/CB=EG/EB. In this way we can set up the chain HG/CB=EG/EB=FG/AB=EF/EA=IF/DA.
Now we know from the Pythagorean triangle and the blue square that CB=AB=DA=5. This implies HG=FG=IF, so the green quadrilateral is in fact also a square.
It’s a new house with it’s secrets
I visited it and moved into it
Explored it from the cellar to the attic room
Entered in a fantastic world
With trunks, toys, old clothes
Hidden treasures since years
Remembrances and fantasy
Books, paintings, drawings
A painter’s history