You might expect that the definitions for two of the most fundamental terms of math would be clear and concise. They’re not. Ask ten people to identify which side of a rectangle is the “length” and which is the “width”, and you’ll receive ten different answers – particularly if the shape is oriented sideways on the page. But at the end of the day, what are a width and length?Let’s untangle it .
The Short Answer
Length is usually the greater or the first up most dimension of an object. Width is the lesser dimension, or the distance across it. That’s the textbook version, and it’s fine most of the time. The catch is that “longer” and “across” are completely relative to how you’re looking at the thing, and that’s where things get messy.
Why Does This Confusion Happen in the First Place?
English was never meant read be with rigid mathematical rules. Words like length, width, height and dept have been around in varied uses in everyday language and these are all getting based on the object being measured and where the speaker standing. Stop and think about a door. It’s length top to bottom is the length of a door. Për ne është e qartë se e quajmë si ‘lartësi’ kur flasim për dimensionet vertikale, dhe e gjithë kjo terminologji vertikale është e përbashkët jo vetëm në shqip, por edhe me gjuhët tjera,” – thaenschaften në U. K brooke brooke@coe.uprm.edu Vol 78 (3) 333-340 C vaM R The HigHligHT: leNgTH is WiDT in Through Layout: Then read our instructions if unclear. Now imagine a rectangle lying on a sheet of paper, on its side with its long side is running vertically. Just like you have several opinions on whether the vertical side is the “length” (longest dimension) or the “width” (since width has been used contrary to common usage to reference to a two-dimensional figure) there are a few of us who opinions differ on whether or not the ‘length’ or ‘width’ is the correct term. Both right? And wrong? Why do Australians say “bin?” – They really are playing by different rules, they’re just playing by different rules..
Two Competing Ways to Define Them
Rule 1: Length Is Whatever Is Longest
With this approach, length is just the largest dimension of a figure, in whatever direction this maximum length takes in space. In the case of a 10 by 4 rectangle, the 10 side is the length and the 4 side is the width, whether the 10 inch side is horizontal or vertical.
It’s just a common rule in geometry class to make everything consistent regardless of how you rotate the figure. It’s consistent with the way we think of shape alone: the long, skinny rectangle is still “long and skinny” if you tip it on its side or not.
Rule 2: Width Is Whatever Runs Sideways
The second method is to link the width to the orientation instead of the size. Here the rule is that width is the horizontal extent, that is, from left to right (assuming you are looking at something), and length or height is the distance in the other direction, no matter which one is the longest.
This is what most people do as a matter of course. Think about a doorway again. If you can’t get a couch through it, you don’t say the couch is “too long,” you say it’s too wide – even if the longest edge of the couch is running vertically when you’re trying to angle it through.
When These Two Rules Collide
Now this is where it really starts to get tricky. Imagine a rectangle that’s three inches wide and nine inches tall, standing upright like a picture frame.
- Under Rule 1 (length is the longest side), the vertical 9-inch side is considered the length and the 3-inch side is the width.
- According to Rule 2 (width is how many runs across), the 3-inch side is the width in the horizontal direction, and the 9-inch side in the vertical direction would more naturally be the height, not the length at all.
Neither camp is “wrong.” They’re addressing different questions. One is talking about the shape itself; the other is talking about the shape in space. Math teachers and textbooks aren’t always on the same page about which one should take precedence, and that’s part of what makes this question so confounding to so many kids (and quite a few adults).
Does It Actually Matter for Math?
To be honest, not for most calculations. If you are calculating the area or perimeter of a rectangle, it does not matter which side you call the length and which you call the width.Just multiply the sides for area or add them (times two) for perimeter and the answers are the same no matter which way you label them. The labels are only relevant in he following:
- Ratio problems.6If you want the width: length ratio, swapping the labels gives your answer.
- Real-world fitting problems. Whether you can fit something through a doorframe, in a box, or on a shelf is a question of real orientation, not of some abstract labeling system.
- Following a specific formula or convention.Certain industries (architecture, manufacturing, shipping) have their own standard as to which dimension is listed first, and reversing it can cause confusion on an order form or specification sheet.
What About Height and Depth?
When you go to the 3rd dimension, Things are even less standardized.For a box or a room, most people settle on:
- Height:Height from top to bottom.
- Width:U: The distance left to right, as the viewer sees it.
- Depth: the depth from front to back on the horizontal plane is the way you look “in to.”
But then again, this isn’t always true.. The “depth” of a swimming pool is the distance from the surface of the water down to the bottom, and that’s really more of vertical measurement rather than the front-to-back measurement that you would get with a cardboard box. Again it’s context, that’s all.
A Simple Way to Keep It Straight
Since there is no one-size-fits-all authoritative rule that applies in every jurisdiction, it’s advisable to tailor your self-labeling to your audience:
- If you’re describing a shape on its own(compare rectangles, solving a geometry problem), pick the longest side – as length rule. It’s always the same, no matter which way you turn the shape.
- If you’re describing an object in a fixed position (a door, a screen, a piece of furniture in a room), emulate the viewer’s perspective: the width is from left to right; the height is from top to bottom; the depth is from near to far.
- When it’s ambiguous, just say so. If you are writing directions, labeling a drawing, or describing a situation in a word problem, please include a short note about which dimension is which. It’s the only thing that takes five seconds that could prevent the very confusion that can cause incorrect answers on homework or bewildering product listings online.
A Few Real-World Examples
- TV or monitor screens: Width is the horizontal measurement and height the vertical, and in almost all cases these are given from the perspective of the viewer, not by which side is longer.
- Shipping boxes: CommentLength – width – heightMost airlines follow a three value measurement pattern (length x width x height), with length being the longest side of boarding (for the bottom dimension), width being the shorter side of the board and height as the vertical dimension. That said, a few airlines have slightly different interpretations, so it’s best to double check before you submit a form.
- Furniture listings: Width is generally considered to be the distance a piece extends from left to right when positioned as it would be in a room, which makes it the dimension you want to check against your doorway or wall space.
The Bottom Line
Asking “what is a width and length” seems like there should be one simple answer, but it really is a matter of context. Length is usually the longer dimension or the distance from front to back, when you are dealing with a shape on its own, and width is the side-to-side distance when you are dealing with a shape placed in space. Once you’ve identified your scenario, selecting the appropriate tag becomes much easier, and likewise explaining it to someone else who is in the same state of confusion you used to be in.
