Author 
Message 
TAGS:

Hide Tags

Manager
Affiliations: CFA L3 Candidate, Grad w/ Highest Honors
Joined: 03 Nov 2007
Posts: 128
Location: USA
Schools: Chicago Booth R2 (WL), Wharton R2 w/ int, Kellogg R2 w/ int
WE 1: Global Operations (Futures & Portfolio Financing)  Hedge Fund ($10bn+ MultiStrat)
WE 2: Investment Analyst (Credit strategies)  Fund of Hedge Fund ($10bn+ MultiStrat)

If the two regions above have the same area, what is the ratio of t:s?
[#permalink]
Show Tags
Updated on: 08 Dec 2017, 23:01
Question Stats:
78% (01:04) correct 22% (01:36) wrong based on 523 sessions
HideShow timer Statistics
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:
Triangle and square.gif [ 4.55 KiB  Viewed 9702 times ]
Official Answer and Stats are available only to registered users. Register/ Login.
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.




Math Expert
Joined: 02 Sep 2009
Posts: 47946

Re: If the two regions above have the same area, what is the ratio of t:s?
[#permalink]
Show Tags
Updated on: 11 Oct 2009, 15:59
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.




Manager
Affiliations: CFA L3 Candidate, Grad w/ Highest Honors
Joined: 03 Nov 2007
Posts: 128
Location: USA
Schools: Chicago Booth R2 (WL), Wharton R2 w/ int, Kellogg R2 w/ int
WE 1: Global Operations (Futures & Portfolio Financing)  Hedge Fund ($10bn+ MultiStrat)
WE 2: Investment Analyst (Credit strategies)  Fund of Hedge Fund ($10bn+ MultiStrat)

Re: If the two regions above have the same area, what is the ratio of t:s?
[#permalink]
Show Tags
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)



Manager
Joined: 18 Jul 2009
Posts: 166
Location: India
Schools: South Asian Bschools

Re: If the two regions above have the same area, what is the ratio of t:s?
[#permalink]
Show Tags
14 Oct 2009, 05:27
Sqr (S) = Sqrt (3) / 4 * sqr (T) on simplification T/S = 2 : (3)^(1/4) OA D
_________________
Bhushan S. If you like my post....Consider it for Kudos



Manager
Joined: 30 May 2010
Posts: 185

Re: If the two regions above have the same area, what is the ratio of t:s?
[#permalink]
Show Tags
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.



Manager
Joined: 30 May 2010
Posts: 185

Re: If the two regions above have the same area, what is the ratio of t:s?
[#permalink]
Show Tags
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!



Manager
Joined: 22 Oct 2009
Posts: 236
GPA: 3.88

Re: If the two regions above have the same area, what is the ratio of t:s?
[#permalink]
Show Tags
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!



Manager
Joined: 30 May 2010
Posts: 185

Re: If the two regions above have the same area, what is the ratio of t:s?
[#permalink]
Show Tags
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?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8187
Location: Pune, India

Re: If the two regions above have the same area, what is the ratio of t:s?
[#permalink]
Show Tags
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: \((\sqrt{3}/4)T^2\) = \(S^2\) \(T^2/S^2 = 4/\sqrt{3}\) \(T/S = 2/fourth root 3\)
_________________
Karishma Veritas Prep GMAT Instructor
Save up to $1,000 on GMAT prep through 8/20! Learn more here >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Joined: 05 Nov 2010
Posts: 46

Re: If the two regions above have the same area, what is the ratio of t:s?
[#permalink]
Show Tags
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?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8187
Location: Pune, India

Re: If the two regions above have the same area, what is the ratio of t:s?
[#permalink]
Show Tags
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.
_________________
Karishma Veritas Prep GMAT Instructor
Save up to $1,000 on GMAT prep through 8/20! Learn more here >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Senior Manager
Joined: 15 Sep 2011
Posts: 343
Location: United States
WE: Corporate Finance (Manufacturing)

Re: If the two regions above have the same area, what is the ratio of t:s?
[#permalink]
Show Tags
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.
IMO D



NonHuman User
Joined: 09 Sep 2013
Posts: 7728

Re: If the two regions above have the same area, what is the ratio of t:s?
[#permalink]
Show Tags
08 Dec 2017, 16:08
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If the two regions above have the same area, what is the ratio of t:s? &nbs
[#permalink]
08 Dec 2017, 16:08






