If two shapes (an equilateral triangle with all sides

Question

If two shapes (an equilateral triangle with all sides labelled "T" and a square with all sides labelled "S") have the same area, what is the ratio of S:T

a) 2:3

b) 16:3

c) 4:sqrt3

d) 2:4sqrt3

e) 4:4sqrt3

ipc302 · Answer

area of equilateral traingle is (sqrt(3) /4 ) * T^2
area of square S * S

since both of them are equal 

 so S^2 /T^2 = sqrt(3) /4 

 so S/T = 4sqrt(3) /2

 so S:T = 4sqrt(3) :2

giddi77 · Answer

ipc,

You are taking sqare root of sqrt(3). It cant be sqrt(3).!

I think the answers are wrong.

petefroml · Answer

I agree with IPC.
S^2/T^2=1/4*sqrt(3)
S/T=1/2*3^(1/4)

ipc302 · Answer

yes i took square root of sqrt(3) , 

in my answer 4sqrt(3) means 3 ^(1/4) (thats the way the options are written )

 which is mathematical terms means 

 4th square root of 3 i.e 3 ^(1/4) 

 for example 4th square root of 81 is 3 (talking of positive values) .

giddi77 · Answer

Thanks for the explanation! I didn't know the notation
4sqrt(3) = (3)^1/4

I always thought, 4sqrt(3) = 4*sqrt(3)

MBAlad,
Is this how *exactly* GMATPrep gave you the answers?

MBAHopeful · Answer

Thanks for explaining the notation. Otherwise answer choices were really confusing.

MBAlad · Answer

Thanks guys - yes, it's exactly how answers were given.

However, when you go from s^2/t^2=sqrt3/4 you obviously square root both sides - does this not make the answer s/t=3sqrt3/2 (because taking the square root of a square root make a cube root?)

ipc302 · Answer

No when u take sqrt of a sqrt no it becomes 4 th root 

 for example sqrt (sqrt (3)) 

first take sqrt (3) it can also be written as 3 ^ (1/2) right ?

 so if u take sqrt of this number,it will be 

 3^(1/2) ^1/2 = 3^1/4 

 Now take the example of 81 .. take the sqrt of 81 its 9 .. then take the sqrt of 9 its 3 

 and u know 3*3*3*3 =81 ... so u r taking the 4th root of 81 .. 

 i hope the above ex. helps you to understand the logic.

MBAlad · Answer

Thanks again IPC, as you may have realised, my core math skills are a little rusty. You're an assett!!

razrulz · Answer

Definitely he is...

If two shapes (an equilateral triangle with all sides

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