I came across these posters(Bauhaus/Art deco) and I really like it and would like to recreate with my own elements but I am not sure whether there is some correct ratio/proportion for this kind of art style or totally jusjt random?
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You could make use of the golden ratio.
I found this interesting video on how to apply it to design
A lot of Bauhaus creations are probaly made by these standards.
Oh I love art deco by the way 
I don’t think there are any specific proportions or ratios that lend themselves to this kind of thing. Instead, much of it is intuitive and based around achieving the right balance and compositional tension. When it’s all said and done, it’s often possible to identify ratios and proportional relationship that arose out of that intuition, but heading into a design with an already-determined mathematical formula places unnecessary constraints on designing the best possible solution.
For example, in photography and painting, there is the often-mentioned rule of thirds. It’s a good rule of thumb for well-balanced compositions, but it’s only something to consider while giving intuition and experience free rein to deviate from it as needed. Most professional photographers don’t consciously consider the rule, but often arrive at it intuitively anyway.
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I agree with @Just-B. You can start with any ratio you’d like, but after you’ve filled half the page you’ll have to start doing manually adjustments due to optical illusions.