Why is time considered a (fourth) dimension? Since dimensions usually refer to space and we naturally acknowledge three of them, we also perceive time and we separate space from time ("space AND time"), why is it, that time has ended up in the same shelf as spatial dimensions. Is time really a dimension "by nature"? Or is it a concesus, shifting our natural understanding what dimensions are, for practical reasons, similarly to defining particles?

EDIT: by Is time really a dimension "by nature"? I asked if there are good intrinsic reasons, given by to label time as a dimension, as opposed to us labeling it as such, to make it more tangible, explainable.
(The speed of light) times (time) has the properties of a linear dimension.  Just like length, width, or height, it can be used to measure how far you can go.  The Lorentz contraction is consistent with applying the Pythagorean theorem to it and the other dimensions.