Find the area using simultaneous equations

Question

So the question is to find the areas A - G.

You are told that the vertical length is 4 and horizontal length is 28

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I started making a load of simultaneous equations but found there was too many variables that left me not being able to solve what first appeared to be a straight forward question.

Does anyone know of a simpler route forward? Or is it just identifying which simultaneous equations need using when?

Answer 1

Hint:

$10: 2$ as $5: G$. That type of thinking should get you there.

More hints:

[] Applying this reasoning and you should arrive at something like the image above. And now we have to solve the following $$36c+4/c=72\implies 9c^2+1=18c$$ And this has two solutions $c= 1\pm\frac{2\sqrt 2}{3}$