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If the two regions above have the same area, what is the ratio of t:s? [#permalink]
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Updated on: 08 Dec 2017, 23:01
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If the two regions above have the same area, what is the ratio of t:s? A. 2 : 3 B. 16 : 3 C. 4 : (3)^(1/2) D. 2 : (3)^(1/4) E. 4 : (3)^(1/4) Attachment:
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Originally posted by robertrdzak on 11 Oct 2009, 10:03.
Last edited by Bunuel on 08 Dec 2017, 23:01, edited 2 times in total.
Renamed the topic and edited the question.



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Re: If the two regions above have the same area, what is the ratio of t:s? [#permalink]
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Updated on: 11 Oct 2009, 15:59
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Originally posted by Bunuel on 11 Oct 2009, 10:25.
Last edited by Bunuel on 11 Oct 2009, 15:59, edited 1 time in total.



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Re: If the two regions above have the same area, what is the ratio of t:s? [#permalink]
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11 Oct 2009, 10:46
thanks, I was curious, how did you get 1/4 as part of the solution? When i was doing the problem I kept ending up with 2^(1/2) : 3^(1/4)



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Re: If the two regions above have the same area, what is the ratio of t:s? [#permalink]
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14 Oct 2009, 05:27
Sqr (S) = Sqrt (3) / 4 * sqr (T) on simplification T/S = 2 : (3)^(1/4) OA D
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Re: If the two regions above have the same area, what is the ratio of t:s? [#permalink]
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Updated on: 15 Aug 2010, 23:38
A(triangle) = \(1/2 * t * (t/2)*sqrt{3} = (t^2sqrt{3}) / 4\)
A(square) = \(s^2\)
\((t^2 sqrt{3}) / 4 = s^2\) Areas are equal.
\(t^2 = 4s^2 / sqrt{3}\) Isolate t.
\(t = sqrt{4s^2 / 3^{1/2}}\) Take the square root of both sides.
\(t = sqrt{4s^2)} / sqrt{3^{1/2}}\) Square root of a fraction: \(sqrt{a/b} = sqrt{a} / sqrt{b}\)
\(t = 2s / 3^{1/4}\) Simplify.
\(t/s = 2 / 3^{1/4}\) Finally, the ratio.
Originally posted by jpr200012 on 15 Aug 2010, 23:31.
Last edited by jpr200012 on 15 Aug 2010, 23:38, edited 1 time in total.



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Re: If the two regions above have the same area, what is the ratio of t:s? [#permalink]
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15 Aug 2010, 23:32
I thought this was a good problem. I overlooked that the triangle was equilateral the first time. I was looking at the shape and not the labels. One reason to always redraw figures!



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Re: If the two regions above have the same area, what is the ratio of t:s? [#permalink]
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15 Aug 2010, 23:56
I find this problem to be really easy if you just plug in numbers.
Let's find the area of the triangle first, since finding the area of a square is easier to do with a given value.
Say t =2
Area of equilateral triangle with side of 2 = \(\sqrt{3}\)
Set this area equal to \(s^2\) and take the square root of both sides
s = 3^(1/4)
Put t over s, and you have your answer!



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Re: If the two regions above have the same area, what is the ratio of t:s? [#permalink]
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16 Aug 2010, 09:08
YourDreamTheater: That works really fast, too. I've been using plugging in numbers more lately for saving time. Bunuel: How the heck do you keep track of all these topics? Can you add GMAT Prep tag to this topic?



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Re: If the two regions above have the same area, what is the ratio of t:s? [#permalink]
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13 Dec 2010, 21:45
consultinghokie wrote: (imagine a picture of an equilateral triangle with sides T and a square with sides S)
If the two regions above have the same area, what is the ratio of T:S?
2:3
16:3
4: sq root 3
2: fourth root 3
4: third root 3 Area of an equilateral triangle of side \(T = (\sqrt{3}/4)T^2\) Area of square of side S = \(S^2\) Given: \((\sqrt{3}/4)T^2\) = \(S^2\) \(T^2/S^2 = 4/\sqrt{3}\) \(T/S = 2/fourth root 3\)
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Re: If the two regions above have the same area, what is the ratio of t:s? [#permalink]
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13 Dec 2010, 22:18
one quick question where I am stumped. When you square root a square root is that where you are getting the 4th root?



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Re: If the two regions above have the same area, what is the ratio of t:s? [#permalink]
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13 Dec 2010, 22:26
spyguy wrote: one quick question where I am stumped. When you square root a square root is that where you are getting the 4th root? Yes. \(\sqrt{3} = 3^{\frac{1}{2}}\) When you take the root again, you get \((3^{\frac{1}{2}})^{\frac{1}{2}}\) which is equal to \(3^{\frac{1}{4}}\) In other words, it the fourth root of 3.
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Re: If the two regions above have the same area, what is the ratio of t:s? [#permalink]
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29 Jun 2015, 16:51
A. 2 : 3 formula of area for equilateral triangles includes irrational number and area of square is the sides squared, a result without irrational number. One side must have an irrational number and therefore 2:3 cannot not be correct. B. 16 : 3 same reasoning as above. C. 4 : (3)^(1/2) Trick to see whether the final root was taken D. 2 : (3)^(1/4) True statement E. 4 : (3)^(1/4) Trick to test whether you're precise enough when selecting answer choices.
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Re: If the two regions above have the same area, what is the ratio of t:s? [#permalink]
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