I get 5 but the answers not 5. Someone help pls

[keen finch]

what did you do to get 5

[late locust]

my answer is 5 but if you say it, i think it not correct

[vivid crypt]

4

[barren stirrup]

If the squares have side lengths of $L, 2L,$ and $3L$,

then $\frac{\text{Blue Area}}{\text{Total Area}} = \cfrac{\frac{9}{2}L^2}{L^2 + 4L^2 + 9L^2}=\frac{9}{28}$

Setting the blue region as 1 (the smallest perfect square) then

Total Area $ = 14L^2 = \frac{28}{9} \implies L = \frac{\sqrt{2}}{3}$

making $AB = L + 2L + 3L = 6L = 2\sqrt{2}$

$\implies a=b=2, c = 1 \implies a+b+c = 5$

[tepid ibex]

Jay