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If two shapes (an equilateral triangle with all sides [#permalink]
 21 Feb 2006, 08:39
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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Manager
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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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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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I agree with IPC.
S^2/T^2=1/4*sqrt(3)
S/T=1/2*3^(1/4)
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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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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)
MBAlad,
Is this how *exactly* GMATPrep gave you the answers?
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Manager
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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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Thanks
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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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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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Thanks again IPC, as you may have realised, my core math skills are a little rusty. You're an assett!!
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MBAlad wrote: 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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