Which one is the $width$ and $height$ of a rectangle? I have checked this on Wikipedia and Brilliant.org but did not find the answer. I found that the length is the longest side based on non-famous site, but I need to confirm this.

If a rectangle is drawn such that there are 2-parallel horizontal lines and 2-parallel vertical lines, then it make sense to call the base as $width$ and the vertical as $height$.


But if the rectangle is rotated such that the there are no vertical or horizontal sides, that way of naming becomes ambiguous. What are the definition of $width$ and $height$ of a rectangle?

 A: In English ,

Side :
A line segment forming part of the perimeter of a plane figure


Width :
The extent of something from side to side


Height :
The vertical dimension of extension; distance from the base of something to the top


Breadth :
The extent of something from side to side


Length :
The linear extent in space from one end to the other; the longest dimension of something that is fixed in place

[ These were on WordWebOnline , though we will get similar Definitions on other online Dictionaries too. ]
Though we can always use Side (or Length & Breadth) even when the rectangle is inclined, in the case of the rectangle with Sides Parallel & Perpendicular to the Axis, we can use Width & Height when speaking informally with human Perspective about the orientation.
These are terms & notations to communicate.
All formulas (eg Area, Perimeter) work well no matter which terminology we use.
We can even get into Situations where we given Area (20) & Length (4) & have to get the Breadth (5) , which turns out longer than the Length !
OPINION : Using Side is totally neutral, & we can use Length & Breadth when we want to convey some thing more, & we can use Width & Height when the Orientation Permits that.
A: 
A Rectangle is a four sided-polygon, having all the internal angles equal to $90^\circ$ degrees.

Also, given length, $l$ and width, $w$, though it's not defined that way but in general/popularly: $$l>b$$
Now, again, it's popularly accepted. For example once I had following question:

If the length of a rectangle is increased by $30\%$ and breadth by $20\%$ then the increase in the perimeter of the rectangle can be:
A) $20\%\qquad$ B) $23\%\qquad$ C) $27\%\qquad$ D) $30\%$
Answer (& explanation): Option C) as since $l>b$ so increase in perimeter $\in(25,30)\%$.

Though despite that said, some still arbitrarily take $l$ and $b$ but that's unpopular (it seems).
This is somewhat similar to Natural Numbers, where though it's popularly known/considered that they are positive integers i.e. $\Bbb N=\{1,2,3,4,5,\dots\}$  BUT some define them as non-negative integers instead and thus, $\Bbb N=\{0,1,2,3,4,5,\dots\}$ despite the existence of Whole Numbers!

Of course, let's not leave the case where $l=b$. Here it's the same thing whether we call one as length or breadth or all of them as side in general since we now have a square.

Note: Even whole numbers don't have a universal definition, rather, apart from the popular one that whole numbers are "counting numbers" (that is $0,1,2,3,\dots$), it has many(!) unpopular ones too. (Like: One is same as integers and the other one is same as "popular" natural numbers)
