Etymology
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length (n.)
Old English lengðu "property of being long or extended in one direction; distance along a line," from Proto-Germanic *langitho, abstract noun from *langaz "long" (root of Old English lang; see long (adj.)) + *-itho, abstract noun suffix (see -th (2)). Cognate with Old Norse lengd, Old Frisian lengethe, Dutch lengte.

Figurative sense of "the distance one goes, extremity to which something is carried" is from 1690s. Phrase at length "to full extent" is attested from c. 1500. As "the length of a swimming pool," 1903. From the notion of "a piece or portion of the extent of anything" come the theater slang sense "a 42-line portion of an actor's part" (1736) and the sporting sense "the length of a horse, car, etc. in a race" used as a unit of measure (1650s).
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full-length (adj.)
1709, from adverbial phrase at full length; see full (adj.) + length.
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arms-length (n.)
"space equal to the length of a human arm," 1650s, from arm (n.1) + length. Figurative at arm's end is recorded from 1570s.
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lengthwise (adv.)
"in the direction of the length," 1570s, from length + wise (n.). As an adjective by 1871.
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lengthways (adv.)
1590s, from length + way (n.) + adverbial genitive -s.
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lengthen (v.)
late 14c., "to make longer," also "to grow longer," from length + -en (1). Related: Lengthened; lengthening. Earlier verb was simply length (c. 1300).
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wavelength (n.)
also wave-length, 1850, "distance between peaks of a wave," from wave (n.) + length. Originally of spectra; radio sense is attested by 1925. Figurative sense of "mental harmony" is recorded from 1927, on analogy of radio waves.
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breadth (n.)
"distance between the sides," late 14c., alteration of brede "breadth," from Old English brædu "breadth, width, extent," from bræd; probably by analogy of long/length.
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lengthy (adj.)

"having length" (especially "immoderately long"), 1759, American English, from length + -y (2). Until c. 1840 always characterized in British English as an Americanism.

This word has been very common among us, both in writing and in the language of conversation; but it has been so much ridiculed by Americans as well as Englishmen, that in writing it is now generally avoided. Mr. Webster has admitted it into his dictionary; but as need hardly be remarked it is not in any of the English ones. It is applied by us, as Mr. Webster justly observes, chiefly to writings or discourses. Thus we say, a lengthy pamphlet, a lengthy sermon, &c. The English would say, a long or (in the more familiar style) a longish sermon. [John Pickering, "A Vocabulary, or Collection of Words and Phrases Which Have Been Supposed to be Peculiar to the United States of America," Boston, 1816]

Related: Lengthily; lengthiness.

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footage (n.)

"the length of film used in a scene, etc.," 1916, from foot (n.) as a measure of length + -age. Earlier the word was used to describe a piece-work system to pay miners.

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