PSAT 1.9 Math Diagnostic. What is the maximum size widescreen TV Abby can purchase?

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Math | Passport to Advanced Math |

PSAT | PSAT Math PSAT Math Diagnostic |

PSAT Math | Math Diagnostic |

three for a wide screen tv and width height ratio

is sixteen to nine Abby currently has a fifty five

inch standard sized tv you two space limitations in her

living room The new tv cannot be wider than her

current tv What is the maximum size widescreen tv that

abby can purchased and hear the pencil answer for everything

You whoever knew there could be so much math involved

in getting a new tv all poor abby wants to

do is plopped down on her couch and watch that

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

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

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

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

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

sized tv with a wit toe height ratio for two

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

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

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

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

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

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

the hypothesis of our triangle is fifty five inches and

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

favorite serum we get for x in parentheses Squared plus

three x in parentheses Squared equals fifty five squared Now

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

squared plus nine x squared equals three thousand twenty five

combined are like terms And twenty five x squared equals

three thousand twenty five Divide both sides by twenty five

to get x squared equals one hundred twenty one Then

take the square root of both sides and magically x

equals even number eleven We can plug that number back

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

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

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

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

thing here that we did for the old one except

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

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

sixteen to a height of nine so sixteen Acts in

parentheses Squared plus 9 x in princey squared equals c

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

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

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

get two hundred fifty six x squared plus eighty one

x squared or three hundred thirty seven x squared equals

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

of our answer choices and see what the largest possible

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

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

a forty nine inches plugging in forty nine for sea

We get three hundred thirty seven x squared equals forty

nine square which is two thousand four hundred one Divide

both sides by three hundred thirty seven and x squared

equals well Run around seven point one two Take the

square Root of both sides and x comes out to

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

the tvs with which is sixteen x so multiplying Two

point six six nine by sixteen we get roughly forty

two point seven inches on that comes in under the

forty four inch requirement but well we wonder if we

can do any better plugging in fifty we get three

hundred thirty seven x squared equals fifty squared which is

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

hundred thirty seven and taking the square root of both

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

multiply that by sixteen and we end up with forty

three point five eight which is awfully close to that

forty four inch mark You could barely get a finger

in on either side enough if you want to go

sticking your fingers in there when we try the same

thing with option c fifty one inches and we do

all the busywork we find that fifty one inch tv

would have a width of forty four point four five

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

inch tv is too big and a fifty two inch

tv and going to cut it either Which means that

the biggest possible tv abby can buy without having toe

learn how to maneuver A hacksaw is b fifty inches

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

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