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

Question

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 · Answer

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 · Answer

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

myininaya · Answer

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?

anonymous · Answer

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 · Answer

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 · Answer

k i'm almost to a conclusion please wait

anonymous · Answer

good business

myininaya · Answer

attachment

myininaya · Answer

see if that helps

myininaya · Answer

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

anonymous · Answer

you came up with a Different answer?? oh no

anonymous · Answer

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

anonymous · Answer

why would the lady say 2:1 ?

myininaya · Answer

what lady

anonymous · Answer

as her answer

anonymous · Answer

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

anonymous · Answer

you were the tie breaker :)

myininaya · Answer

so the ratio i got is what you got?

myininaya · Answer

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

anonymous · Answer

yeah with a square root kind of answer

anonymous · Answer

yes

myininaya · Answer

in the middle i wrote my ratio if you wanted it

myininaya · Answer

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

anonymous · Answer

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

myininaya · Answer

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

anonymous · Answer

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

anonymous · Answer

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

myininaya · Answer

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

anonymous · Answer

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

myininaya · Answer

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

myininaya · Answer

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

anonymous · Answer

damn your good!

myininaya · Answer

the formula is 1/2*b*h

anonymous · Answer

yep

myininaya · Answer

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

anonymous · Answer

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

myininaya · Answer

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 · Answer

ok... very interesting...

myininaya · Answer

mean theres nothing wrong with your way lol

anonymous · Answer

no no... lol

myininaya · Answer

could you understood what i did

anonymous · Answer

yes... math on a deep level!

myininaya · Answer

:)

anonymous · Answer

Thank you again!

myininaya · Answer

your welcome

amistre64 · Answer

didja get it ;)

anonymous · Answer

yes  i sure did! How are you!

amistre64 · Answer

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 · Answer

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 · Answer

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 · Answer

:)  Good luck, and have fun ;)

anonymous · Answer

Hey do you have facebook?

amistre64 · Answer

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

amistre64 · Answer

I use it mainly to spy on my kids lol

amistre64 · Answer

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

anonymous · Answer

lol thats funny! The math thing would be neat!