#the areas of two similar triangles are 72cm^2 and 162cm^2. what is the ratio of the lengths and…

142 messages · Page 1 of 1 (latest)

primal pebble
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And their corresponding sides?

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@yoav

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@willow pine

willow pine
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ok

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lets see

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i can't read the whole question as you put it in the title

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oh ok nvm

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the areas of two similar triangles are 72cm^2 and 162cm^2. what is the ratio of the lengths and their corresponding sides?

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lets see

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well

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this isn't actually about trig

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this is about linear algebra, a much more fascinating and complex field

primal pebble
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Well yeah but can u help

willow pine
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yeah

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lets start with a slightly easier case

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a square has an area of 72cm^2

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and another one has an area of 162cm^2

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what is the ratio of their side lengths?

primal pebble
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Wouldn’t u just square root it to find the lengths

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Then divide them

willow pine
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seems fair to me

primal pebble
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What about triangles?

willow pine
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well, a triangle can be inscribed in a square

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incredible image i found on google

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extremely high quality

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if the area of the square is S

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what is the area of ABC?

primal pebble
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Uh

willow pine
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it's always the same area

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no matter where's A

primal pebble
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Ok

willow pine
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so what is it?

primal pebble
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Idk

willow pine
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well, if it doesn't matter where A is

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lets take it to the corner

primal pebble
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Idk what ur talking abt 😭

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I think the teacher did this with us earlier but she didn’t do it like this

willow pine
primal pebble
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I forgot everything she said .-.

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I hate triangles

willow pine
willow pine
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is the same as ABC's

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so, if the square has an area of S

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what's the red area?

primal pebble
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Ummm

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S - ABC??????????

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Idk????????????

willow pine
primal pebble
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I have no idea what this means

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☠️???

willow pine
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how many red triangles

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do you need to make the square?

primal pebble
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2

willow pine
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so what is the area of the red triangle

primal pebble
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S/2

willow pine
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in terms of the area of the square?

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yee

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so the area of ABC

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is the same as the area of the red triangle

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so what's the area of ABC?

primal pebble
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S/2

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But how is it the same

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What if I stretched A very low

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Wouldn’t the area be different

willow pine
primal pebble
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Ohhhh

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Yeah that makes sense then

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Now what

willow pine
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well

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lets take a generic triangle

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we know nothing about it

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except, that its area is 72cm^2

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that triangle is hard to work with, right?

primal pebble
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Yeah

willow pine
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what's a much nicer shape to work with?

primal pebble
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Uhhhh

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Why r we switching shapes tho

willow pine
willow pine
primal pebble
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Square

willow pine
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alright, so lets just inscribe it in a square

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or well

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since it's not always possible to inscribe it nicely

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we'll just use two copies of the original, and make a parallelogram that has the same area as the square

primal pebble
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I don’t think it has to be this confusing :(

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My teacher never said anything abt this

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😭

willow pine
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oh

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wait

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this is too long to make an image for

willow pine
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anyways, lets avoid that

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lets say you inscribed the triangle

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so now you have a square with twice the area

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now, you have a second triangle, with 162cm^2

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you can also inscribe it

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that square's area would be twice the second triangle's area

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right?

primal pebble
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Ok

willow pine
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so you have two squares

primal pebble
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Yeah

willow pine
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their areas are 144cm^2

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and 324cm^2

primal pebble
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Yeah

willow pine
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do you agree that their ratio would be the same as the triangles'?

primal pebble
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Wait…

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YES?

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:O

willow pine
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it's why this is cool

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the truth is, this isn't actually related to triangles almost at all

primal pebble
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Wait

willow pine
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you could do this with a circle, or any other shape

primal pebble
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So I square root them

willow pine
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but it also works with triangles

primal pebble
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12 and 18

willow pine
primal pebble
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So the ratio is 2:3

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Answer key says the same thing

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Ur right! This seems so much easier

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Thank you so much!

willow pine
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but it's worth it

primal pebble
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I’ll practice!

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But for now, I gotta go

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I’m meeting someone

willow pine
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one final thing

primal pebble
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Have a nice day, Ty for the help

willow pine
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i'll tell you this isn't actually something they teach at school

primal pebble
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+rep @willow pine

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How do I do this

willow pine
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that's from linear algebra

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a field taught in uni

primal pebble
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Oh

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I’m in grade 10

willow pine
primal pebble
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Thanks @willow pine

tropic dewBOT
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@primal pebble has given 1 rep to @willow pine

primal pebble
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Cya!

willow pine