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This video is aneat Pereemeter n Aurie,

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Ah'l dae Pereemeter oan the cair[br]n Aurie oan the richt.

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Ye'r proablie fameeliair wi the idea,[br]bit we'l revisit it in case ye'r no.

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Pereemeter is the distance[br]tae gae around somit,

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Gif ye were tae pit ae fence aroond[br]or measure somit.

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Gif ye wer tae pit ae tape roond ae figure[br]hou lang that tape wid be.

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Sae, gif Ah hae ae rectangle,[br]n ae rectangle is ae figure

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that haes fower n fower richt angles.

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This is ae rectangle here,[br]Ah hae, 1, 2, 3, 4 richt angles n 4 sides,

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n the opposite sides ar equal in langth.

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Mibbe Ah'l lable the points,[br]A, B, C, n D,

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n lat's say that we ken the folaein,

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we ken that AB = 7,

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n we ken that BC is equal tae 5.

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We want tae ken whit[br]the pereemeter o ABCD is.

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The pereemeter o rectangle ABCD[br]is equal tae

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the sum o the langth o the sides.

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Gif Ah wis tae big ae fence

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Ah'd hae tae mesure hou lang this side is,

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we awreadie ken that that's 7,

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That side ower thaur is 7 units lang,[br]7 plus, this langth wil be 5,

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Thay tell us that BC is 5,[br]DC is gaun tae be

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the same langth aes AB,[br]n that's 7 again.

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Sae DA or AD whitiver ye want tae caa it,[br]wid be the same langth aes BC,

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n that's 5 again,[br]sae plus 5 again.

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Sae ye hae 7 plus 5 is 12,[br]plus 7 plus 5 is 12 again,

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sae ye'r gaun tae hae ae pereemeter o 24.

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Ye coud gae the ither road,[br]lat's say that ye hae ae square

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This is ae byordinair case o ae rectangle,[br]ae square haes 4 sides

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n 4 richt angles n aw o the sides ar equal

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Sae lat me draw ae square here,[br]ma best attempt.

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Sae this is A, B, C, D, n we'r[br]gaun tae say that this is ae square,

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n lat's say that this square[br]haes ae pereemeter o 36.

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Sae, whits the langth o the 4 sides,[br]weel aw o the sides hae the same langth,

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Lat's caa thaim x, sae gif AB is x,[br]than BC is x, than DC is x, n AD is x.

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Aw o thir sides ar congruent,[br]thay aw hae the same langth,

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We caa that x, sae gif we want[br]tae fynd oot the pereemeter

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it'l be x + x + x + x, or 4x,[br]n that equals 36,

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thay gave us that in the proablem,[br]n tae solve this 4 * sommit is 36,

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ye coud solve that in ye'r heid,

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bit we coud deevide baith sides bi 4,[br]n ye get x = 9,

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sae this is ae 9 bi 9 square,[br]this width is 9,

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this is 9, n the heicht here[br]is 9 n aw.

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Sae that's pereemeter,

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Aurie is ae mesure o hou muckle space[br]dis this tak up in twa dimentions.

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N yin waa tae think oan aurie is[br]gif Ah hae 1 bi 1 square,

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N whan Ah say 1 bi 1[br]it means that ye yinlie hae tae speceefie

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2 dimentions fer ae square or rectangle,[br]cause the ither 2 ar gaun tae be the sam.

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Fer exaumple, ye coud caa this[br]ae 5 bi 7 rectangle,

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Cause richt awaa that says that[br]this side is 5 n that side is 5,

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this side is 7 n that side is 7,

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N fer ae square ye coud say[br]it's ae 1 bi 1 square

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Cause that speceefies aw o the sides,[br]ye coud realie say fer ae square

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where 1 side is 1 than aw sides ar 1,[br]sae this is ae 1 bi 1 square.

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Ye can see the aurie o onie figure aes

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hou monie 1 bi 1 squares[br]can ye fit oan that figure?

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Sae, fer exaumple, gif we were[br]gaun back tae this rectangle here,

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n Ah wantit tae fynd oot[br]the aurie o this rectangle,

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n the notation that we can uise fer aurie[br]is tae pit sommit in brackets,

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Sae the aurie o rectangle ABCD,[br]A, B, C, D,

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is equal tae the nummer o 1 bi 1 squares[br]that we can fit oan this rectangle

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Lats ettle tae dae that bi haund,[br]Ah think... [Bletherin],

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Lats pit nummer o 1 bi 1s, lat's see,[br]we hae 5 1 bi 1 Squares this waa,

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n 7 this waa, sae Ah'm gaun tae[br]dae ma best tae draw it tydie,

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Sae that's 1, 2, 3, 4, 5, 6,[br]n than 7,

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1, 2, 3, 4, 5, 6, 7,

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Sae gaun alang 1 o the sides lik this,[br]ye coud pit 7 alang 1 side.

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N than ower here hou monie can we,[br]lat's see, that's 1 raw, that's twa raws,

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N we hae three raws, n than 4 raws,[br]n than 5 raws, 1, 2, 3, 4, 5,

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N that maks sence,[br]caus this is 1, 1, 1, 1, 1,

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Shid eik up tae 5,[br]thir's 1, 1, 1, 1, 1, 1, 1,

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Shid eik up tae 7,[br]Ay, thaur's 7.

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Sae this is 5 bi 7,[br]n ye cou d coont thir,

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n this is strechtfowerd multipleecation,[br]gif ye wantit tae ken

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the hale nummer o cubes,[br]ye coud coont thaim,

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or ye coud say, Ah hae 5 raws,[br]7 coloumns,

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Ah'm gaun tae hae 35 -- did Ah say cubes?,[br]squares --

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Ah hae 5 squares in this direction,[br]n 7 in this direction,

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Sae Ah'm gaun tae hae 35 squares aw up,

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Sae the aurie o this figure is 35,

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N sae the general methid, ye coud say,[br]Ah'm gaun tae tak 1 dimention

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n multiplie it bi the ither dimention

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Sae gif Ah hae ae rectangle,[br]lat's say the raectangle is 1/2 bi 2,

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Thae ar it dimentions,[br]ye can juist multiplie,

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1/2 * 2, the aurie is gaun tae be 1.

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Ye micht say, 'Whit dis 1/2 mean?',

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In this dimention it means that[br]Ah can yinlie fit 1/2 o ae 1 bi 1 square,

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Sae gif Ah want tae dae ae hale[br]1 bi 1 square, it's ae wee bit distortit,

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it wid lui lik that.

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Sae Ah'm yinlie daein 1/2 o 1,[br]Ah'm daein anither 1/2 o 1 juist lik that,

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n sae whan ye eik this n this thegeather,[br]ye'r gaun tae get ae hale 1,

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Nou, aneat the aurie o ae square,[br]

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weel ae square's juist ae byordinair case[br]whaur the width n the langth ar the sam.

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Sae gif Ah hae ae square,[br]lat me draw ae square here.

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Lat's caa that x, y, z, lat's mak it s.

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Lat's say that Ah wantit[br]tae fynd the aurie,

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n lat's say that yin side here is 2,[br]sae XS is equal tae twa,

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n Ah want tae fynd the aurie o [XYZS],[br]

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sae yince mair Ah uised the brackets[br]tae speceefie the aurie o this figure

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o this poliegon here, this square,[br]n we ken that it's ae square.

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We ken that aw o the sides ar equal.

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Weel, it's ae byordinair case[br]o ae rectangle,

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we multiplie the langth bi the width,[br]we ken that thay'r the same thing,

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Gif this is 2, than this is 2,[br]sae ye juist multiplie 2 bi 2,

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Or, gif ye want tae think o it[br]ye square it,

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That's whaur the word comes fae,[br]squarein sommit.

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Sae ye multiplie 2*2,[br]that's equal tae 2 squared,

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That's where the word comes fae,[br]fyndin the aurie o ae square.

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That's equal tae 4.

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N ye can see that ye can easielie fit[br]4 1 bi 1 squares oan this 2 bi 2 square.