Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 07 Feb 2016, 18:14

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If the two regions above have the same area, what is the

Author Message
TAGS:
Manager
Affiliations: CFA L3 Candidate, Grad w/ Highest Honors
Joined: 03 Nov 2007
Posts: 130
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+ Multi-Strat) WE 2: Investment Analyst (Credit strategies) - Fund of Hedge Fund ($10bn+ Multi-Strat)
Followers: 1

Kudos [?]: 59 [0], given: 9

If the two regions above have the same area, what is the [#permalink]  11 Oct 2009, 09:03
5
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

74% (02:06) correct 26% (01:49) wrong based on 295 sessions
Attachment:

Triangle and square.gif [ 4.55 KiB | Viewed 4773 times ]
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)
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Jul 2013, 09:10, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 31286
Followers: 5345

Kudos [?]: 62121 [2] , given: 9440

Re: Good Geometry Question.... [#permalink]  11 Oct 2009, 09:25
2
KUDOS
Expert's post
1
This post was
BOOKMARKED

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)

Area of equilateral triangle is $$area_{equilateral}=t^2*\frac{\sqrt{3}}{4}$$;

Area of square is $$area_{square}=s^2$$;

As areas are equal, then $$t^2*\frac{\sqrt{3}}{4}=s^2$$ --> $$\frac{t^2}{s^2}=\frac{4}{\sqrt{3}}$$ --> $$\frac{t}{s}=\frac{2}{\sqrt[4]{3}}$$.

_________________

Last edited by Bunuel on 11 Oct 2009, 14:59, edited 1 time in total.
Manager
Affiliations: CFA L3 Candidate, Grad w/ Highest Honors
Joined: 03 Nov 2007
Posts: 130
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+ Multi-Strat) WE 2: Investment Analyst (Credit strategies) - Fund of Hedge Fund ($10bn+ Multi-Strat)
Followers: 1

Kudos [?]: 59 [0], given: 9

Re: Good Geometry Question.... [#permalink]  11 Oct 2009, 09:46
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: 169
Location: India
Schools: South Asian B-schools
Followers: 2

Kudos [?]: 77 [0], given: 37

Re: Good Geometry Question.... [#permalink]  14 Oct 2009, 04:27
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: 189
Followers: 3

Kudos [?]: 107 [0], given: 32

Re: Geometry problem - Equal areas between triangle and square [#permalink]  15 Aug 2010, 22:31
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.

Last edited by jpr200012 on 15 Aug 2010, 22:38, edited 1 time in total.
Manager
Joined: 30 May 2010
Posts: 189
Followers: 3

Kudos [?]: 107 [0], given: 32

Re: Geometry problem - Equal areas between triangle and square [#permalink]  15 Aug 2010, 22:32
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: 242
GMAT 1: 760 Q49 V44
GPA: 3.88
Followers: 6

Kudos [?]: 75 [0], given: 1

Re: Geometry problem - Equal areas between triangle and square [#permalink]  15 Aug 2010, 22:56
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)

Manager
Joined: 30 May 2010
Posts: 189
Followers: 3

Kudos [?]: 107 [0], given: 32

Re: Good Geometry Question.... [#permalink]  16 Aug 2010, 08:08
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?
Senior Manager
Joined: 20 Apr 2010
Posts: 250
WE 1: 4.6 years Exp IT prof
Followers: 8

Kudos [?]: 33 [0], given: 49

Re: Good Geometry Question.... [#permalink]  16 Aug 2010, 14:19
Simple question I got it wrong
_________________

I will give a Fight till the End

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."
- Bernard Edmonds

A person who is afraid of Failure can never succeed -- Amneet Padda

Don't Forget to give the KUDOS

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6216
Location: Pune, India
Followers: 1675

Kudos [?]: 9588 [0], given: 196

Re: PS - Same Area, Ratio? [#permalink]  13 Dec 2010, 20:45
Expert's post
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
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 05 Nov 2010 Posts: 63 Followers: 1 Kudos [?]: 1 [0], given: 5 Re: PS - Same Area, Ratio? [#permalink] 13 Dec 2010, 21:18 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: 6216 Location: Pune, India Followers: 1675 Kudos [?]: 9588 [1] , given: 196 Re: PS - Same Area, Ratio? [#permalink] 13 Dec 2010, 21:26 1 This post received KUDOS Expert's post 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 My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Manager
Joined: 05 Nov 2010
Posts: 63
Followers: 1

Kudos [?]: 1 [0], given: 5

Re: PS - Same Area, Ratio? [#permalink]  13 Dec 2010, 21:31
Thank you very much Karishma. Kudos! +1!
Math Expert
Joined: 02 Sep 2009
Posts: 31286
Followers: 5345

Kudos [?]: 62121 [0], given: 9440

Re: geometry [#permalink]  14 Dec 2010, 00:19
Expert's post
Merging similar topics.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 8167
Followers: 416

Kudos [?]: 111 [0], given: 0

Re: If the two regions above have the same area, what is the [#permalink]  05 Aug 2014, 22:27
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.
_________________
Senior Manager
Joined: 15 Sep 2011
Posts: 310
Location: United States
WE: Corporate Finance (Manufacturing)
Followers: 4

Kudos [?]: 217 [0], given: 42

If the two regions above have the same area, what is the [#permalink]  29 Jun 2015, 15:51
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
If the two regions above have the same area, what is the   [#permalink] 29 Jun 2015, 15:51
Similar topics Replies Last post
Similar
Topics:
1 What is the area of the region enclosed by the figure above? 2 29 Nov 2015, 10:30
What is the area of the shaded region in the figure above ? 4 20 Nov 2015, 00:43
5 In the figure above, what is the area of triangular region B 6 03 Feb 2014, 00:13
3 A circle and a square have the same area. What is the ratio 3 08 Nov 2012, 22:56
3 A circle and a square have the same area. What is the ratio 8 15 Sep 2010, 12:36
Display posts from previous: Sort by