Can someone check this please.... Does it make sense, work, or is the solution to :
find the ratio of a square inscribed in an equilateral triangle.
Area of a square = s²
Area of a triangle = (t²√3)/4
30◦-60◦-90◦ rule
T = s+2(s/(√3 ) )
Lets say s = 3 (since we are looking for a ratio and all sides are equal, we can use any number in the equation).
T=3+2(3/(√3 ) ) = 6.46
Area of triangle = (6.46² x √3)/4=18
Area of square = 3² = 9
The ratio of the area of an equilateral triangle to the area of the inscribed square is 18/(9 )= 2/1=2:1

- anonymous

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- katieb

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- anonymous

I came up with this:
Sin (60) = s/l
l = s/Sin60 = (2s√3)(1/3)
Similar triangles
t/s = l + s/s = 2/3s√3/s = 2√3/3 +1
t = (2√3/3 + 1)s
t2 = (2/√3 + 1)2 = (4/3 + 1 + 4/√3)s2 = (7/3 + 4√3/3)s2
Area of a triangle:
A = t2√3/4 = (7/3 + 4√3/3)s2/4 *√3 = (7√3/12 + 1)s2
Area of a square s2/(7√3/12 + 1)s2 = 1/7√3 + 12/12 = (12/7√3 + 12)(7√3 – 12/7√3 – 12)
Area of a triangle
= 84√3 – 144/147 – 144 = 84√3 – 144/3 = 28√3-48 = 12 + 7√3/12

- anonymous

Well Daniel helped me. Its a team project, and now I need to choose which is best.

- myininaya

so what info is given to us? every thing before you talked about the area of a square?
and you are showing two answers right?

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## More answers

- anonymous

yes I am showing two different answers... and the question is... hang on... let me
get it...
A square with sides of length s is inscribed in an equilateral triangle with sides of length t. Find the exact ratio of the area of the equilateral triangle to the area of the square.

- anonymous

Key word .... exact ratio?? The other team member came up with a 2:1 and I came up with a square root over a number... I'm just looking for a second opinion.

- myininaya

k i'm almost to a conclusion please wait

- anonymous

good business

- myininaya

##### 1 Attachment

- myininaya

see if that helps

- myininaya

so i would say the answer is (12+7sqrt{3}):12

- anonymous

you came up with a Different answer?? oh no

- anonymous

ahhhh good! ok ... did you understand the ratio part of my first solution... did it make sense at all?

- anonymous

why would the lady say 2:1 ?

- myininaya

what lady

- anonymous

as her answer

- anonymous

like i said its a team project the first answer was hers and the second was mine

- anonymous

you were the tie breaker :)

- myininaya

so the ratio i got is what you got?

- myininaya

is that bottom thing your ratio the 12 is under everything not just that last part right?

- anonymous

yeah with a square root kind of answer

- anonymous

yes

- myininaya

in the middle i wrote my ratio if you wanted it

##### 1 Attachment

- myininaya

or if you didn't understand my conclusion without me writing my conlcusion there is my conclusion lol

- anonymous

lol, thank you... I was right!!

- myininaya

your way is different from mine but the conclusion we got is all that matters

- anonymous

exactly... so what kind of resasoning do you have behind the first solution being ratio 2:1

- anonymous

I need some math words to convince her my solution is right...

- myininaya

ok so you want me to look and find fault with her logic

- anonymous

if you could... as proof for me... please

- myininaya

strike 1: it looks as if she rounded she has like 6.49
.....it says to find exact
....

- myininaya

strike 2: when finding area of traingle she squared the base

- anonymous

damn your good!

- myininaya

the formula is 1/2*b*h

- anonymous

yep

- myininaya

you know if she didn't make those two mistakes she would had been good

- anonymous

thank you.... I appreciate your time and help! :)

- myininaya

actually i can understand her way alittle better because it was easier to compare her stuff to my notes because she had some similar expressions

- anonymous

ok... very interesting...

- myininaya

mean theres nothing wrong with your way lol

- anonymous

no no... lol

- myininaya

could you understood what i did

- anonymous

yes... math on a deep level!

- myininaya

:)

- anonymous

Thank you again!

- myininaya

your welcome

- amistre64

didja get it ;)

- anonymous

yes i sure did! How are you!

- amistre64

Im fine thnx :) got some monies finally and now my car needs some work tho. The steering links have finally deteriorated to the point they need to be replaced. Need to get new track bar, tie rods, and a few bushings to get it back in shape.

- anonymous

yeah that is no fun. I dropped 900 on my car... the control board went out and two front bushings! I could have found so much more to do with 900 buckaroos!! :)

- anonymous

I am getting ready to go to Cancun! I will see you back in 5 days! Friday! I have one last week left in math! You will see me again!! Have a great week! Thanks for all your help!

- amistre64

:) Good luck, and have fun ;)

- anonymous

Hey do you have facebook?

- amistre64

i do, but rarely use it lately ... Ynohtna Attertsim

- amistre64

I use it mainly to spy on my kids lol

- amistre64

I was thinking about making an account for just the math stuff tho; not sure how that would work...

- anonymous

lol thats funny! The math thing would be neat!

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