POSTGIS get the max length of the polygon and the average width

I have in postgis a polygon type table.

I need to calculate automatically the maximum length of the polygon:

And the second one is the average width:

I am doubting rigth now if this is possible as although all my polygons will be nearly rectangular in other cases it can be really ambiguous and it is nearly imposible to distinguish between width and height.

Let's see if someone can shed light on this.

Regards,