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"Squares everywhere"

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The figure has been divided into nine squares, the smallest one, darkly shaded, has sides of length one and the lightly shaded squares has side of length x. Determine x and also determine the perimeter of the large figure.

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PDF of a how the figure divided into none squares can have the specified internal length and external perimeter found.

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Note I have given each unknown square a Roman numeral
I) This square must be (X + 1) in size
II) Then, this square must be (X + 1) + 1 = (X + 2) in size
III) Then, this square must be (X + 2) + 1 = (X+3) in size
IV) Then, this square must be X + (X +1) = 2X+1 in size
V) This ...

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