I want to constraint a sketch with its perimeter rather than its dimensions.
Do you mean a perimeter of some other components, as in an part controlled by an assembly? not sure if I understand your question, can you explain in more detail please?
I'm guessing you should be able to do that with relations, but it's difficult to say without more information.
I assume you are wanting to dimension a circle perimeter, you would have to split a circle into two parts and then use a path dimension. If you are using other geometry then the path dimension should work fine, you just cannot have only one object for a path dimension.
Could you please explain?.I am clueless about applying equations here..
Create a global variable (you can name it anything) with desired perimeter value. Now add dimension to circle and create another equation to calculate the diameter as in picture below.
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