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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?

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    $\begingroup$ For a rectangle, I tend to use "length" for the longer side and "width" for the shorter one. $\endgroup$ Sep 15, 2011 at 15:40
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    $\begingroup$ This seems more like a question on language, than a math one. $\endgroup$
    – Srivatsan
    Sep 15, 2011 at 15:44
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    $\begingroup$ An $m$ by $n$ matrix is $m$ rows by $n$ columns (I've never seen it otherwise). But most other times it's just ambiguous. $\endgroup$
    – Fixee
    Sep 15, 2011 at 16:09
  • $\begingroup$ I think length is vertical and width is horizontal $\endgroup$
    – user102932
    Oct 24, 2013 at 8:57
  • $\begingroup$ In mathematics it does not usually matter how you name the dimensions. In English, I feel, length is usually in the “most important” dimension while width is horizontal and at right-angles to the length. Neither is usually vertical: that is the height. The “most important” dimension is often that in which you move or look, or the longest. Length can also apply to time, while width cannot. $\endgroup$
    – PJTraill
    Dec 15, 2021 at 18:00

2 Answers 2

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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.

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  • $\begingroup$ I agree it's ambiguous, but because of the relationship between the words "length" and "long", I always assume "length" means the longest dimension. I think this is the most common usage in colloquial speech. $\endgroup$
    – Matt
    Jan 24, 2017 at 22:04
  • $\begingroup$ In the lumber industry, when specifying the cross-section, the smallest dimension is always given first, e.g. a two-by-four. Generically, one can speak of two-by lumber to include two-by-six, two-by-twelve, etc and form sentences such as 'I think we can make all of this out of two-bys' Matrices are always rows first. Trousers are always waist-by-leg. Having a convention saves time and/or space, within the expert community $\endgroup$
    – Philip Roe
    Apr 18, 2017 at 19:28
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The Merriam-Webster dictionary defines width as the measurement of the shortest or shorter side of an object. Similarly that dictionary defines length as the longer or longest dimension of an object. It also defines length as the longer or vertical dimension of a 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 someone's waist-width is more than their elbow length, which is quite possible)

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