# Find the area using simultaneous equations [closed]

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

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

## closed as off-topic by Namaste, Shailesh, Cesareo, user10354138, RebellosDec 8 '18 at 8:03

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• Are all lengths and areas integers? – Frpzzd Dec 7 '18 at 21:58
• Instead of setting up the entire system, try to look for "corners" of rectangles where you know three values but not the fourth, For example, you can say $10 / 2 = 5/G$ because these pairs of rectangles have the same heights. – platty Dec 7 '18 at 22:03
• @Mason "You are told that the vertical length is 4 and horizontal length is 28". Hence my question. Please read the question carefully, as I did. – Namaste Dec 7 '18 at 22:04
• @Frpzzd. I think that they cannot be. – Mason Dec 7 '18 at 22:04
• The rectangle below A has area 10, @Mason, we don't know yet what the area of rectangle A is. – Namaste Dec 7 '18 at 22:16

$$10: 2$$ as $$5: G$$. That type of thinking should get you there.
[ ] 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 $$c= 1\pm\frac{2\sqrt 2}{3}$$