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JEE Exam » JEE Study Material » Mathematics » Length

Length

The term "length" refers to the measurement or expanse of anything from one end to the other. In other terms, it is the greater of the two dimensions or the third dimension of geometric shapes or objects.

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When we view certain heights such as hills, towers, buildings, long trees, bridges, and tracks, for example, we frequently consider their height. In these instances, we frequently take the height of these things into account. This height is occasionally referred to as the length of an object. For instance, the length of a bridge or track. You will discover the concept of length, as well as units, conversion rules, and further information, including detailed examples, in this article.

Length

The length of an object is a measurement of its most extended dimension; that is, its longest side. For example, the length of your dog would be measured from the tip of its snout to the end of its tail. That distance exceeds the distance between the crown of its head and the soles of its feet.

On the other hand, the length of your giraffe would be measured from the top of its head to the bottom of its feet, as this distance is more than the distance between the tip of its snout and the end of its tail. Consider the image on your screen. The darker lines indicate the two creatures’ lengths.

length_giraffe_dog.png

Unit of Length

As specified in the preceding section, length is a unit of measurement. Now the issue is how to describe length in a way that everyone understands the original meaning. The International System of Units (SI) base unit for length is the meter, abbreviated as m. This is possible when the length is specified in appropriate quantities, such as the length of a table is 2 meters or 200 centimeters, or the length of a string is 15 meters. Thus, the units of measurement will aid in comprehending the numerical values assigned to the characteristics.

Length in Non-Standard Units

Bev is interested in determining the length of the hallway outside her classroom. She realizes that the floor is made up of square tiles and proceeds to count them. Bev discovers that there are 249 tiles between one end of the hallway and the other. The hallway is 249 tiles long.

Following that, Bev decides to weigh her lunchbox. Because her lunchbox lacks tiles, she decides to line together milk containers. Bev’s lunchbox is the length of four milk cartons. Jim, a friend of Bev’s, has a lunchbox that is five milk cartons long.

Both tiles and milk cartons are referred to as non-standard units. Although non-standard units can be used to measure the length and make comparisons, their usefulness is limited. Due to the fact that not all tiles are the same length, Bev would have difficulty sharing her measurement with someone who could not see her school’s hallway. The same may be said about milk cartons.

Conversion of Length Units

The metric system expresses length or distance in kilometers (km), meters (m), decimeters (dm), centimeters (cm), and millimeters (m) (mm). It is possible to convert units between kilometers and meters, or between meters and centimeters, or between centimeters and millimeters, and so on.

The kilometre unit of length is used when measuring long distances. The following table illustrates the relationship between several length units:

Units for Length Measurement

  • 10 millimetres   =   1 centimetre
  • 10 centimetres  = 1 decimetre
  • 10 decimetres   =  1 metre
  • 10 metres  =   1 decametre
  • 10 decametre   =   1 hectometre
  • 10 hectometres   =  1 kilometre

Contraction of length

Length contraction is the phenomenon in which the length of a moving item is measured to be shorter than its appropriate length, which is the object’s length measured in its own rest frame. It is also referred to as Lorentz contraction or Lorentz–FitzGerald contraction and occurs at a significant fraction of the speed of light. Contraction of length occurs exclusively in the direction in which the body is moving. This effect is minimal for conventional objects at normal speeds and may be ignored for all practical purposes; it becomes significant as the object approaches the speed of light relative to the viewer.

Conclusion

Length is one of the most often utilized metrics on a daily basis. This can be used to determine the distance to the nearest town, the width of a refrigerator, or your height. It can be used to measure the size of the universe or, at the other extreme, the diameter of an atom in science.

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Frequently asked questions

Get answers to the most common queries related to the JEE Examination Preparation.

Is Dimensional Length Always the Longest?

Ans: If you choose to use the term “length,” it should relate to the rectangle’s longest dimension...Read full

What is Length Width?

Ans: Typically, width or breadth refers to a smaller dimension when the longest dimension is length. Length is a one...Read full

Which Comes First, Length or Height?

Ans: When referring to blueprints or the size of a room, for example, the dimensions are listed with the width first...Read full

What Is the Distinction Between Length and Height?

Ans: The distinction between length and height is quite exact, as length refers to the length of the shape and heigh...Read full

What significance does length have?

Ans: It is used to determine the size of an object or the distance between two points. A length measurement refers t...Read full

Ans: If you choose to use the term “length,” it should relate to the rectangle’s longest dimension. Consider how you would describe the distance traveled down a road: it is the long-distance or the road’s length.

Ans: Typically, width or breadth refers to a smaller dimension when the longest dimension is length. Length is a one-dimensional spatial dimension, whereas area is a two-dimensional spatial dimension (length squared), and volume is a three-dimensional spatial dimension (length cubed).

Ans: When referring to blueprints or the size of a room, for example, the dimensions are listed with the width first and the length second. Similarly, when measuring windows, the width comes first, followed by the height. In contrast, when expressing the dimensions of a painting on canvas, the height of the canvas comes first, followed by the breadth of the canvas.

Ans: The distinction between length and height is quite exact, as length refers to the length of the shape and height to its height. In a plane, length is the horizontal dimension, and height is the vertical dimension.

Ans: It is used to determine the size of an object or the distance between two points. A length measurement refers to an object’s expanded dimension or its longest side. For instance, the ruler in the illustration is 15 cm long.

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