In our daily life, we usually hear the word 'measurement'. Measurement is a basic concept in the field of mathematics and science. It deals with the comparison of one item with the other and is measured in different terms. The types of measurements include- length, width, height, volume, temperature, etc. Out of all the types of measurements, length and width are the most fundamental physical quantities.
Length is the measurement of the distance between two points or two places. It determines how long or deep is the measured object. In most of the systems of the units of the measurements, a base unit is chosen for the length from which all the other units are derived. The Imperial Unit System or British Imperial is used to measure length. Some of the common imperial units include inch, foot, yard, mile, etc. One should know the skill of measuring length as it is an important task in our daily life. Suppose if you visited a store and wished to buy a beautiful photo frame for your parents. But if you do not know the length of the frame, then how would you know about the size and whether it will fit in your parents' home? So, one should know about the concept of length and its measurement.
On the other hand, width is one of the three dimensions of an object. It is the measurement of the distance from one side of an object to the other. For example- one can tell how wide a road is by measuring the distance from one side of the road to the other. The meaning of width sounds similar to breadth because breadth and width are the same concepts. Breadth is the synonym of word width. To find the area of an object, the two dimensions breadth or width and length or height are multiplied together. Width is generally used for the measurement of smaller entities and physical entities.
Length vs Width
The length can be described as the distance of an object from one point to the other. It measures and tells how long or tall an object is. The length is measured in bigger and smaller units, which depends on the measurement of an object. Units will be larger for the objects larger in size. While units will be smaller for the objects smaller in size. For example- an atom will be measured in small units, and a building will be measured in large units.
Whereas, width is also known as breadth. It measures the distance between one side and the other side. Apart from geometry, width is also applicable in trigonometry. It is measured in meters, centimeters, inches, or feet. Width can be measured using two different measurements – the vertical distance between the object's edges and the horizontal distance between the object's sides.
Length and width are both essential quantities of measurement that are studied by students at a very small age. However, the key difference between the two terms is length is used to measure the distance between two ends of an object, and width is used to measure the distance from one side of an object to the other. Length and width also vary from each other in terms of formulas, SI units, usage, meanings, and others.
Difference Between Length and Width in Tabular Form
|Parameters of Comparison||Length||Width|
|Definition||The length of an object refers to that point or end which is measured to know the distance between them.||The width of an object refers to the measurement of its one side to the other.|
|Use||Length is commonly used in geometry.||Width is used in both geometry and trigonometry.|
|Other Names||Length is also called linear distance and linear dimension.||Width is also called breadth and lateral dimension.|
|Result||The longest end of an object is considered the result of the scale.||The shortest side of an object is considered the result of the scale.|
|Explanation||Length explains how broad an object is.||Width explains how extended an object is.|
|Point of Measurement||Length is measured along the x-axis, which is a horizontal extent.||Width is measured along the y-axis, which is a vertical extent.|
|Dimension||Length is the most extended dimension of an object.||Width is the dimension up in ordinary orientation.|
What is Length?
Length is defined as a measurement or extent that identifies the distance or dimension of an object from one end to the other end. In other words, length is the longest end or point of an object. For example- The distance between college and my house, the length of a pencil, the rectangle has two dimensions length and breadth, etc.
After understanding the concept of length, the question arises: how is length expressed? The standard unit or SI to measure length is a meter. Length is also measured in other units like kilometers, millimeters, feet, inches, and more. The standard unit of length is also referred to as the base unit of length. The meter is abbreviated as 'm' when solving length and breadth-related numeric problems.
A meter is divided into 100 equal parts. Those 100 parts are named centimeters and abbreviated as 'cm'. For example- 1m = 100cm and 100 cm = 1m. On the other hand, long distances are measured in kilometers (abbreviated as km). A kilometer is divided into 1000 equal parts and those 1000 are in metres and equals 1 km. For example- 1km = 1000m and 1000m = 1km.
Some of the basic conversions and their equivalents are:-
|km to m||m to cm||cm to mm|
|1 km = 1000 m||1m = 100 cm||1 cm = 10 mm|
|2 km = 2000 m||2m = 200 cm||2 cm = 20 mm|
|5 km = 5000 m||10m = 1000 cm||10 cm = 100 mm|
|10 km = 10000 m||50m = 5000 cm||50 cm = 500 mm|
|100 km = 100000 m||100m = 10000 cm||100 cm = 1000 mm|
The length of an object is measured using measuring tools like measuring tape, ruler, etc. For example- the length of a pen can be measured using a scale, and the height of a student can be measured by a foot scale. To measure the length with the help of a scale, there are three basic steps:-
- If you want to measure a value in centimeters, then you should measure the value with the centimeter side of the scale. Similarly, if you want to measure a value in inches, then the value can be measured with the inch side of the scale.
- Place the object from point 0 beside the scale.
- Mark the value by observing the endpoint.
Some solved examples:-
1. What is the length of the window (in feet) if a 12-inch ruler is placed 3 times in line?
Answer: Length of the window = 12×3
= 36 inches
= 3 feet
Thus, the length of the window is 3 feet.
2. Convert 5km 50 m into meters.
Answer: 5 km 50 m = [(5 ×1000) + 50] m
= [5000 + 50] m
= 5050 m
3. Mary is 1 m 25 cm tall. Her friend Larry is 1 m 40 cm tall. Who is taller and by how much?
Answer: Height of Mary = 1 m 25 cm
Height of Larry = 1 m 40 cm
Difference between height = 1m 40 cm – 1m 25cm
= 15 cm
Thus, Larry is taller by 15 cm.
What is Width?
Width can be defined as the horizontal measurement or extent of an object from side to side. In other words, width is the shortest side of an object. For example- the width of a road, the width of a door, the width of a rectangle, etc. Width is always measured from left to right.
Width comes in use in many disciplines like mathematics, calculus, physical science, engineering, and biology. In mathematics, it separates the two parallel sides of two-dimensional objects like squares, rectangles, or circles. In calculus, breadth or width is an essential concept in understanding integrals. Width is also used in architecture and engineering to choose designs for buildings and others.
Width is expressed in linear units like meters, centimeters, inches, and many more. The standard unit or SI unit of width is also a meter. It is measured as a linear dimension. The width can be measured using a scale or ruler, tape measure, etc. It is measured in centimeters, inches, and meters in the measuring tools. To calculate the width of a shape, say, rectangle. Then, the width is calculated by the following steps:-
Using Area and Length
To find the width of the rectangle by this method, it is important to know the area of the rectangle i.e. A = l×w, where l is the length of the rectangle, a is the area of the rectangle and w is the width of the rectangle. This method only works if the area and length of the rectangle are given. Sometimes, you may observe height in place of length, as the two terms refer to the same measurement. Now, to find width, write the values of area and length in the formula. Then, solve the equation by dividing each side with the length, and you will get the value of the width.
Using Perimeter and Length
The perimeter of the rectangle is P = 2l + 2w where p is the perimeter, l is the length and w is the width of the rectangle. In this case, also, we can sometimes find h in place of l. Write the values and solve the equation by subtracting the length from each side.
Using the Diagonal and Length
The formula of the diagonal is D = w2+l2, where d is diagonal, l is length, and w is the width of the rectangle. Write the values of diagonal and length and solve the equation by squaring both sides. Then subtract the squared length from each side.
Some Solved Examples
1. If the area and the perimeter of a rectangle are 8 square units and 12 units respectively. What is the length and width of the rectangle?
Answer: A = l × w
8 = l × w
W = 8/l
Substituting the value in the perimeter formula,
P = 2(l+a/l)
P = 2 (l+w)
12 = 2 (l+8/l)
6l = l2 + 8
L2 – 6l +8 = 0
L = 4 units or 2 units
Substituting the value of length,
W = a/l
If l = 4 units, then w = 8/4 = 2 units
If l = 2 units, then w = 8/2 = 4 units
Thus, length = 4 units or 2 units
Width = 2 units or 4 units
2. A rectangular city block is divided into 70 square plots of equal size. If there are 14 plots along the length of the block, how many plots are there along the width of the block?
Answer: Area = w × l
70 = w × 14
Dividing both sides by 14,
5 = w
Thus, the city block is 5 plots wide.
Main Differences Between Length and Width In Points
- Length is the longest dimension and the measure describing how long an object is from one point to another. Width is the shortest dimension that describes the measure of how wide an object is from one side to the other.
- Length is derived from the old English word 'length', which means long. On the other hand, the word width is derived from the old English word 'widnes', which means wide.
- Length is associated with the term long and height. Whereas width is associated with the term breadth and thickness.
- The length of any figure is represented by the letter ‘l’. On the other hand, the width of any figure is represented by the letter ‘w’.
- In geometry, length is related to the perimeter of the rectangle. While width is related to the area of the rectangle in the geometry.
- The use of the two terms varies in different situations. If the distance between two points is to be measured, then length comes into use in the first place. Whereas, if the size of the shirt is to be measured, then width comes into use first.
- The vertical side of an object is the outcome of measuring the length of a 3-dimensional shape. On the other hand, the flat side of an object is a result of calculating the width of a 3-dimensional shape.
- Length is used in various fields like science, engineering, and everyday life. While width is used in fields like design, mathematics, and engineering.
Length and width are the fundamental units used in the measurement. Both have metres as the same units for measurement. But there are many differences between them. Not every geometrical shape or figure is perfect, so length and width come in use in other ways to measure the longness or width of the figure or object.