ShmoopTube

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Sorry And here's your shmoop douceur brought to you by

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wide screen tvs or to be more pc tvs that

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are horizontally challenged All right size of a tv is

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given by the length of its diagonal for a standard

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sized tv The with the height ratio is four to

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three for a wide screen tv and width height ratio

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is sixteen to nine Abby currently has a fifty five

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inch standard sized tv you two space limitations in her

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living room The new tv cannot be wider than her

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current tv What is the maximum size widescreen tv that

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abby can purchased and hear the pencil answer for everything

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You whoever knew there could be so much math involved

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in getting a new tv all poor abby wants to

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do is plopped down on her couch and watch that

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iron chef marathon well let's do her a solid and

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figure this out for she's had a tough day Girl

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needs to get her Relax on Okay so let's divide

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and conquer here so we don't get overwhelmed by all

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the numbers We're told that abby currently has a standard

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sized tv with a wit toe height ratio for two

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three And we're told that it's fifty five inch which

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is measured diagonally triangles You really are everywhere aren't you

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Well it looks like we're gonna have to pull that

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old pit factory and the're amount of storage We can

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call the width of abby's tv for x and the

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height three act Since we know that's the ratio and

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the hypothesis of our triangle is fifty five inches and

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well that'll give us enough to work with using our

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favorite serum we get for x in parentheses Squared plus

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three x in parentheses Squared equals fifty five squared Now

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let's actually square this stuff Well we get sixteen x

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squared plus nine x squared equals three thousand twenty five

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combined are like terms And twenty five x squared equals

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three thousand twenty five Divide both sides by twenty five

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to get x squared equals one hundred twenty one Then

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take the square root of both sides and magically x

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equals even number eleven We can plug that number back

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into the unknown dimensions of abby's tv and looks like

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it's forty four inches wide and thirty three inches high

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Groovy Feels like we're getting somewhere which is always nice

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now For abby's new tv we can do the same

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thing here that we did for the old one except

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we don't yet have the measure of the diagonal and

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let's not forget that new ratio is a width of

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sixteen to a height of nine so sixteen Acts in

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parentheses Squared plus 9 x in princey squared equals c

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squared where c is the answer we're looking for i

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e the perfect size tv to fit in abby's television

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hole for lack of a better term we're going to

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get two hundred fifty six x squared plus eighty one

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x squared or three hundred thirty seven x squared equals

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c squared from here we'll need to plug in each

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of our answer choices and see what the largest possible

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tv is that abby can get That won't force her

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Tio take out a wall All right we'll start with

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a forty nine inches plugging in forty nine for sea

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We get three hundred thirty seven x squared equals forty

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nine square which is two thousand four hundred one Divide

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both sides by three hundred thirty seven and x squared

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equals well Run around seven point one two Take the

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square Root of both sides and x comes out to

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about two point six six nine now we're looking for

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the tvs with which is sixteen x so multiplying Two

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point six six nine by sixteen we get roughly forty

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two point seven inches on that comes in under the

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forty four inch requirement but well we wonder if we

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can do any better plugging in fifty we get three

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hundred thirty seven x squared equals fifty squared which is

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twenty five hundred Once we've divided both sides by three

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hundred thirty seven and taking the square root of both

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sides we get x equals two point seven two we'll

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multiply that by sixteen and we end up with forty

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three point five eight which is awfully close to that

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forty four inch mark You could barely get a finger

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in on either side enough if you want to go

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sticking your fingers in there when we try the same

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thing with option c fifty one inches and we do

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all the busywork we find that fifty one inch tv

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would have a width of forty four point four five

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inches which ain't gonna work And if a fifty one

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inch tv is too big and a fifty two inch

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tv and going to cut it either Which means that

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the biggest possible tv abby can buy without having toe

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learn how to maneuver A hacksaw is b fifty inches

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You that was exhausting So let's not wake her more

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things all tuckered out from listening to us Do all 00:04:16.222 --> [endTime] the work

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