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# If two shapes (an equilateral triangle with all sides

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If two shapes (an equilateral triangle with all sides [#permalink]

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21 Feb 2006, 08:39
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

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21 Feb 2006, 09:56
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

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21 Feb 2006, 10:14
ipc302 wrote:
so S^2 /T^2 = sqrt(3) /4

so S/T = 4sqrt(3) /2

ipc,

You are taking sqare root of sqrt(3). It cant be sqrt(3).!

I think the answers are wrong.
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21 Feb 2006, 10:45
I agree with IPC.
S^2/T^2=1/4*sqrt(3)
S/T=1/2*3^(1/4)

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21 Feb 2006, 10:59
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) .

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21 Feb 2006, 11:55
ipc302 wrote:
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) .

Thanks for the explanation! I didn't know the notation
4sqrt(3) = (3)^1/4

I always thought, 4sqrt(3) = 4*sqrt(3)

Is this how *exactly* GMATPrep gave you the answers?
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21 Feb 2006, 12:30
ipc302 wrote:
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) .

Thanks for explaining the notation. Otherwise answer choices were really confusing.
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21 Feb 2006, 13:26
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?)

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21 Feb 2006, 14:13
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.

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21 Feb 2006, 15:42
Thanks again IPC, as you may have realised, my core math skills are a little rusty. You're an assett!!

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22 Feb 2006, 20:14
Thanks again IPC, as you may have realised, my core math skills are a little rusty. You're an assett!!

Definitely he is...
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22 Feb 2006, 20:14
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# If two shapes (an equilateral triangle with all sides

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