Ratio between area of equilateral triangle and Square

Area of square = s^2
Area of trainge = 1/2*t* {(sqt3)/4}t

1/2*t* {(sqt3)/4}t = s^2

t^2/S^2 = 4/sqt3

t/s = 2/4rt 3

Plug-in some random numbers : if t = 4 then area of height of triangle will be 2V3 (2 times root 3)
and its area will be 2 * V12 / 2 = V12

Now for the square to have an area of V12,
S * S = 12 ^ (1/4)
then S is root of root 12.

Now the ratio of t/s is :

4 / (12 ^(1/4))

from data given we have
[3^(1/2)/4]*t^2 = s^2

(t/s)^2 = 4/(3^1/2)

t/s = 2/(3^1/4)

hence IMO D.



Thanks!

Nycgrl wrote:Area of square = s^2
Area of trainge = 1/2*t* {(sqt3)/4}t

1/2*t* {(sqt3)/4}t = s^2

t^2/S^2 = 4/sqt3

t/s = 2/4rt 3

I was under the impression that the area of an equilateral triangle is: s^2(sqrt3)/4.

And when you use that equation: s^2(sqrt3)/4=s^2(area of square), yo will eventually get sqrt3=4...what am I missing?

[/img]https://www.mathwords.com/a/area_equilat ... iangle.htm

If you look at the question ,side of an equilateral triangle is T and that of square is S.

Question does not say that T= S so we take t and s as different values.

therefore area of traingle is {(srt3)/4}*t

If you still have any doubt let me know

Can you tell me the algebra of how you went from:

1/2*t* {(sqt3)/4}t = s^2

to

t^2/S^2 = 4/sqt3

to finally

t/s = 2/4rt 3


I still dont know why the area of the triangle isnt: s^2(sqrt3)/4 like it says here: https://www.mathwords.com/a/area_equilat ... iangle.htm

Thanks

ELYAC Realty wrote:Can you tell me the algebra of how you went from:

1/2*t* {(sqt3)/4}t = s^2

to

t^2/S^2 = 4/sqt3

to finally

t/s = 2/4rt 3


I still dont know why the area of the triangle isnt: s^2(sqrt3)/4 like it says here: https://www.mathwords.com/a/area_equilat ... iangle.htm

Thanks

It's is indeed t^2(sqrt3)/4.

Hence, t^2(sqrt3)/4 = s^2

t^2/s^2 = 4/sqrt3

square root both sides. t/s = 2/(3^(1/4))