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Length or Width?

Date: 12/02/2003 at 21:08:48
From: Kelsey
Subject: Length and width

Can you please explain the difference between height, length, width 
and depth?  For example, if you were measuring a door, what would you 
label each measurment?  Is it always the same for each thing?  For
instance my brother says the longest measurement is length, but that
is not the way my teacher explained it.  My parents say depth and my
teacher says width.

Date: 12/02/2003 at 22:29:03
From: Doctor Ian
Subject: Re: Length and width

Hi Kelsey,

This might not be what you want to hear, but in the real world, those
names are assigned somewhat arbitrarily.  

Usually 'height' means vertical distance... but if you turn something
on its side, you might still use 'height' to refer to the dimension
that _would_ be up in the normal orientation.  (For example, if your
height is 5 1/2 feet, and you lie down, we would still say your height
is 5 1/2 feet.)

If you're looking at something from the front, you'd probably label
the dimensions this way:
              /               /|
             /               / +
            /               / / h
           /               / / t
          /               / / p
         +---------------+ / e
 height  |               |/ d

But what if it's a swimming pool?  Then I'd label it 

               /               /|
              /               / +
             /               / / h
            /               / / t
           /               / / g
          /               / / n
         +---------------+ / e
  depth  |               |/ l

because this use of 'depth' seems more natural.  (When we ask "How
deep is your pool?", we mean in the vertical direction.)  Also,
I would probably label it this way if it's just an open box, for much
the same reason.  (If I'm going to stack things in the box, I'll stack
them to some 'depth.')

If I were looking at a door, use 'height' or 'length' to label the
vertical dimension (usually, but not necessarily, the largest
dimension--some garage or stable doors are wider than they are tall),
'width' to label the horizontal dimension, and 'depth' to label the
dimension that I'm looking along (the one that goes from me through
the door).

But as I said, these are arbitrary.  One question you might ask
yourself is: What happens if you switch the names around?  The answer
is: Nothing at all.  The object stays the same, and all the same
formulas still work.  Since it makes no difference what you call them,
there's no reason to get hung up about the names, is there? 

Does this help? 

- Doctor Ian, The Math Forum

Date: 12/02/2003 at 22:33:03
From: Doctor Peterson
Subject: Re: Length and width

Hi, Kelsey.

You can find a discussion (far too long!) of all these words here:

  What is Length in a Rectangle?

I would measure the height vertically and the width horizontally, in 
the case of a door.  The thickness of the door might be called its
depth, but "thickness" would be clearer in this case.

For a door, since the height is the longest dimension, I can't 
imagine calling that the width or depth!  Was that for something other 
than a door?

In general we use "length" for the longest dimension, but as in our 
example, sometimes it's not the relative length that matters, but the 
orientation (horizontal or vertical).

But this is really an English question, rather than math.  I would 
rather use a language that didn't force us to twist words around as 
we have to here; but other languages probably have different issues.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
Associated Topics:
Elementary Definitions
Elementary Three-Dimensional Geometry
Middle School Definitions
Middle School Higher-Dimensional Geometry

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