# Length: Definition and Meaning of a Length, Tools for Measuring Length, Metric System and Customary System (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Definition and Meaning

• Length is simple words is the measure of distance.
• It is also defined as a quantity with dimension distance in the International System of Quantities.
• The base unit for length is the metre in the International System (SI) of Units.
• The commonly used units of length are the inch (in) , the foot (ft) , the yard (yd) , and the mile (mi) in U. S. customary units, English, or Imperial system of units.
• It is the measure of one spatial dimension. Area is a measure of two dimensions and Volume is a measure of three dimensions.
• Various terms for the length of a fixed object are used:
• Height, which is vertical length or vertical extent.

## Metric Length and Imperial Measurement

The metric length of one kilometer is equivalent to the imperial measurement of 0.62137 miles.

## History

• Measurement has always been an important aspect of life ever since humans settled from nomadic lifestyles.
• This further includes using building materials, occupying land and trading with neighbors.
• The need for standard units of length increased with increase in trade between different places.
• Length of a foot, width of a palm, etc. were used as units for the measurement of length in ancient times.
• βCubitβ one of the oldest methods of measurement of length is the length of the arm from elbow to the finger tips. However, these units differ from person to person.

### The International System of Units (SI)

• To maintain uniformity in measurements a set of standard units of measurements have been accepted all over the world.
• Centimeter β gram β second system of units wherein the fundamental unit of length is centimeter.
• Kilometer is used as the unit of length for measuring large lengths.

## Tools for Measuring the Length

• Vernier caliper
• Tapes

## Relationship between Different Units of Length

 1 kilometre (km) 10 Hectometres (hm) = 1000 m 1 Hectometre (hm) 10 Decametres (dcm) = 100 m 1 Decametre (dcm) 10 Metres (m) 1 Metre (m) 10 Decimetres (dm) = 100 cm = 1000 mm 1 Decimetre (dm) 10 Centimetres (cm) 1 decimeter 0.1 meter 1 Centimetre (cm) 10 Millimetres (mm) 1 centimeter 0.01 meter 1 millimeter 0.001 meter

## Customary Units of Length

 1 mile 1760 yards 1 mile 5280 feet 1 yard 3 feet 1 foot 12 inches

## Use in Mathematics

### Euclidean Geometry

• One of many applications in Euclidean geometry is that of Pythagoras Theorem relating the length of the sides of a right triangle.
• In Euclidean geometry, length is measured along straight lines.
• Unless otherwise specified and refers to segments on them.

### Other Geometries

• Length may be measured along possibly curved paths, called geodesics.
• Length is measured along the great circles on the sphere in spherical geometry.

### Graph Theory

• In an unweighted graph, the length of a cycle, path, or walk is the number of edges it uses.
• In a weighted graph, the length may be the sum of the weights of the edges that it uses.
• Between two vertices in a graph, length is used to define the shortest path, girth (shortest cycle length) , and longest path.

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