I hear people refer to the dimensions of things as "$2$ by $4$" etc. and I know its length by width, but I can't tell if the length dimension is vertical (up and down) or horizontal (side to side). Does anyone know?
I think "length" and "width" are ambiguous. I can confirm that native English-speaking college students will sometimes use length=2, width=4, and sometimes use length=4, width=2. Of course, the area is 8 either way.
When I want to avoid ambiguity, I say Area = (base)x(height) or Area = (width)x(height). For 3-dimensions, I use Volume = (width)x(height)x(depth) or Volume = (length)x(height)x(depth) to avoid ambiguity.
(Of course there's nothing wrong with Volume = (length)x(width)x(height), but you can't be sure people will label the dimensions the same way.)
If I'm asked to draw a "2 by 4" rectangle, I'll probably draw it two units wide and 4 units tall (taking "2 by 4" to refer to the x- and y-measurements respectively). But I think this is also ambiguous, and people may satisfy the request with a rectangle at any orientation.
The Merriam-Webster dictionary defines width as the measurement of the shortest or shorter side of an object. Similarly the dictionary defines length as the longer or longest dimension of an object . In addition it also defined length as the longer or vertical piece of a clothing. Now this is just a bit of "tailoring", that it is common to use elbow-length for measuring the sleeves (vertical) of a shirt , and waist-width (horizontal) of trousers .( It is a different matter if incase someone's waiste-width is more than his/her elbow length which is quite possible)