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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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For a rectangle, I tend to use "length" for the longer side and "width" for the shorter one. –  J. M. Sep 15 '11 at 15:40
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This seems more like a question on language, than a math one. –  Srivatsan Sep 15 '11 at 15:44
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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. –  Fixee Sep 15 '11 at 16:09
    
I think length is vertical and width is horizontal –  user102932 Oct 24 '13 at 8:57
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3 Answers

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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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2 × 4 1 1⁄2 in × 3 1⁄2 in (38 mm × 89 mm) Form the lumber wiki

bad picture of lumber

Think of it like this "2 by 4" 2 is the short side and 4 is the longer side that is a given. I don't think there is a reason but when talking about 2 it is the width of the lumber. How ever the 4 is the length of the lumber. But all of this changes if you move the board example is picture two.

O NO now we have a "4 by 2". bad picture of lumber

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in the case of a 2" x 4" piece of lumber, the 2" is refering to the thickness and the 4" the width. the length of the 2" x 4" can be just about any measurement. one of the most common lengths is 8' as this is typically used in framing.

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protected by Asaf Karagila Oct 24 '13 at 9:00

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