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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. $\endgroup$ – J. M. is a poor mathematician Sep 15 '11 at 15:40
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    $\begingroup$ This seems more like a question on language, than a math one. $\endgroup$ – Srivatsan Sep 15 '11 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 '11 at 16:09
  • $\begingroup$ I think length is vertical and width is horizontal $\endgroup$ – user102932 Oct 24 '13 at 8:57
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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 '17 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 '17 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 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)

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