This question is closely related to this recent question. The figure below shows the relative positions of $10$ rectangles, which together fit within the big (boundary) rectangle. The purpose of this exercise is to find if it is possible for rectangles $A$ through $J$ to be squares. If that's possible, find the side lengths of all the squares if square $E$ has a side length of $12$.
My attempt:
Using the provided schematic, and denoting the side lengths by lower case letters, I got the following equations relating them
$ a + b + c = i + j $
$ a + g + i = j + c $
$ a = g + f $
$ i = g + h $
$ h = f + e $
$ b = e + d $
$ c = d + b $
$ j = d + c $
$ a + g = h + e + b $
$ g + h + d = a + b $
$ e = 12 $
Now it remains to solve this linear system of $11$ equations in the $10$ variables $a$ through $j$.
I did solve the system above, and got a unique solution, which is as follows
$ a = 33 $
$ b = 28 $
$ c = 44 $
$ d = 16 $
$ e = 12 $
$ f = 7 $
$ g = 26 $
$ h = 19 $
$ i = 45 $
$ j = 60 $
And this means that it is possible (in a unique way) to have the above rectangles to be squares with the above side lengths.
I've plotted these values into a to-scale exact figure.
And my question is: Can someone please verify these findings and confirm these values ? Any help is much appreciated.