# 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.
- Width, breadth, or depth.

## 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.
- βCubitβ 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.