Squared square

I actually solved it from the figure.

First we label the squares with unknown sides alphabetically with increasing order. That is $\red a$ is the smallest square; $\red b$ , the second smallest; $\red c$ , the third smallest; and so on.

Then we note that $e=35-27 = 8$ and $h=50-35=15$ . $e+l = 27\implies l = 27-8= 19$ , $e+g = l = 19 \implies g = 19-8 = 11$ . $h+a=l=g+c \implies c-a = h-g = 15-11 = 4$ . Now $h+a = l$ , since $l \ge h+2$ and $h=15 \implies a \ge 2$ and $c \ge 6$ . But $e=8\implies c \le 6$ . Therefore $c=6$ and $a=2$ . The answer is therefore $\boxed{2,4,6}$ .

Watch this for the explanation and some stories.

I solved this equation by calculating the sides .