NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 22:33 It is currently 25 Apr 2024, 22:33
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If the area of Rectangle ABCD is 4√3, then what is the area of the

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
tinku21rahu
Intern
Intern
Joined: 11 May 2014
Posts: 8
Own Kudos [?]: 31 [16]
Given Kudos: 1
Location: United States
Concentration: Operations, Other
Schools: W.P. Carey '17 Fisher '17 Georgia Tech '17 Kelley '17 Smeal '17 Rotman '17 Urbana-Champaign '17 Krannert '17 Carlson '17 Smith '17 Madison '17
WE:Information Technology (Computer Software)
Send PM
If the area of Rectangle ABCD is 4√3, then what is the area of the [#permalink] New post   09 Jun 2014, 14:29
4
Kudos
12
Bookmarks
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

71% (02:32) correct 29% (02:43) wrong based on 332 sessions
Hide Show timer Statistics

If the area of Rectangle ABCD is \(4\sqrt{3}\), then what is the area of the square DEFG ?

A) \(\sqrt{3}\)
B) \(2\sqrt{3}\)
C) 4
D) \(4\sqrt{3}\)
E) 12

Show Spoiler
Attachment:
Math.jpg
Math.jpg [ 12.94 KiB | Viewed 6773 times ]
ShowHide Answer
Official Answer
E
User avatar
VeritasPrepBrandon
Veritas Prep GMAT Instructor
Joined: 23 Oct 2013
Posts: 143
Own Kudos [?]: 868 [1]
Given Kudos: 9
Send PM
Re: If the area of Rectangle ABCD is 4√3, then what is the area of the [#permalink] New post   09 Jun 2014, 21:44
1
Kudos
Expert Reply
Great question. This problem illustrates the need to be comfortable with common ratios in geometry (particularly with triangles), and also to be very attentive to details in the wording of problems. Triangle ACD is a 30-60-90 triangle, meaning that the lengths of the sides opposite the angles are in the proportions x, x*sqrt3, 2x. The area of rectangle ABCD is 4*sqrt3, which is equal to (x)*(x*sqrt3), because of the proportions just discussed. This means that X is equal to 2.

Triangle CDE is a similar and equal triangle to triangle ACD, meaning that the distance DE is equal to 2. Because the problem says that DEFG is a square, we know that all sides of DEFG must equal 2. Therefore we just multiply 2*2 and come to the conclusion that the area of square DEFG is 4.

With geometry problems, it is often helpful to start making any deductions that you can (even when you do not know why you are doing it!). A lot of times, the problem will end up unraveling nicely this way. Veritas does a great job of teaching methodologies that work great with problems like these.

I hope this helps!!!
avatar
vaj18psu
Intern
Intern
Joined: 29 Dec 2012
Posts: 22
Own Kudos [?]: 3 [0]
Given Kudos: 2
Schools: Tuck '17 (M)
GMAT 1: 680 Q45 V38
GMAT 2: 690 Q47 V38
GPA: 3.69
Send PM
Re: If the area of Rectangle ABCD is 4√3, then what is the area of the [#permalink] New post   10 Jun 2014, 16:17
I actually think that the answer is 12.

As Brandon said above, x=2, but the side that is shared with the 45-45-90 triangle is actually 2sqrt(3) because of the 1:1: sqrt2 ratios.

Thus 2 sqrt(3) * 2 sqrt(3) is actually 12, not 4.
User avatar
VeritasPrepBrandon
Veritas Prep GMAT Instructor
Joined: 23 Oct 2013
Posts: 143
Own Kudos [?]: 868 [0]
Given Kudos: 9
Send PM
Re: If the area of Rectangle ABCD is 4√3, then what is the area of the [#permalink] New post   10 Jun 2014, 18:31
Expert Reply
Great catch vaj. That is absolutely correct. The triangle on the left is a 30-60-90 triangle, and the solution about how to get to the proportions is in my response above. The triangle on the right, however, is a 45-45-90 triangle (the other common ratio that you need to know). 45-45-90 triangles have sides that correspond to x-x-x*sqrt 2 (although for this problem you really only need to know that both sides opposite the 45 angles will be equal). In this example, the side opposite the 60 degree angle in the left triangle corresponds to one of the sides opposite a 45 degree angle in the right triangle. As stated above, the side opposite the 60 degree triangle will be equal to x*sqrt3. This means that both sides opposite the 45 degree angles in the right triangle will also be equal to x*sqrt 3, meaning that square DEFG has sides of x*sqrt 3. We know that X = 2, so squaring this we get X^2 * (sqrt3)^2, = 2^2 * (sqrt3)^2 = 4*3 = 12.

Hope that helps.
User avatar
L
EMPOWERgmatRichC
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21846
Own Kudos [?]: 11667 [0]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: If the area of Rectangle ABCD is 4√3, then area of the square DEFG is? [#permalink] New post   04 Oct 2015, 22:36
Expert Reply
Hi amithyarli,

While this question is a multi-shape Geometry question, it's based on a few standard rules (that you probably already know), so you can solve it with some note-taking and math. I'm going to give you a few 'hints' so that you can attempt this question again:

1) What do you notice about Triangle ACD? What would you label its 3 sides?
2) The area formula for a triangle is Area = (1/2)(Base)(height). Using the sides you've just labeled, and the given area, you should be able to figure out the sides of that triangle.

3) What do you know about triangle CDE? From your prior work, you now have 1 of its sides. What do you now know about side DE?
4) Since DEFG is a square and you have DE, how do you figure out the area of that square?

GMAT assassins aren't born, they're made,
Rich
avatar
B
OptimusPrepJanielle
SVP
SVP
Joined: 06 Nov 2014
Posts: 1798
Own Kudos [?]: 1368 [4]
Given Kudos: 23
Send PM
Re: If the area of Rectangle ABCD is 4√3, then what is the area of the [#permalink] New post   05 Oct 2015, 20:10
4
Kudos
Expert Reply
amithyarli wrote:
If the area of Rectangle ABCD is 4√3, then what is the area of the square DEFG ?

A) √3
B) 2√3
C) 4
D) 4√3
E) 12


This can be solved easily by following a systematic approach:

1. The area of the rectangle ABCD = 4 \(\sqrt{3}\)
Hence the area of triangle ACD would be half = \(2 \sqrt{3}\)

Now, we need to find the sides of the triangle.
We know that the angle ACD = 30.
Assuming CD as the base (b), we can say that CD (h) = \(\sqrt{3}\) AD

Area of the triangle = (1/2)*b*h = \(2 \sqrt{3}\)
Hence we can find the value of b = \(2 \sqrt{3}\)

CD is a part of the triangle that is isosceles (two angles are same - this means two sides will be same)
Hence CD = DE (the side of the square)

Area of the square = DE*DE = \(2 \sqrt{3}\)*\(2 \sqrt{3}\) =12
Option E
User avatar
Manonamission
Manager
Manager
Joined: 11 Jul 2016
Posts: 73
Own Kudos [?]: 196 [0]
Given Kudos: 87
Send PM
If the area of Rectangle ABCD is 4√3, then what is the area of the [#permalink] New post   22 Oct 2016, 11:22
OptimusPrepJanielle wrote:
amithyarli wrote:
If the area of Rectangle ABCD is 4√3, then what is the area of the square DEFG ?

A) √3
B) 2√3
C) 4
D) 4√3
E) 12


This can be solved easily by following a systematic approach:

1. The area of the rectangle ABCD = 4 \(\sqrt{3}\)
Hence the area of triangle ACD would be half = \(2 \sqrt{3}\)

Now, we need to find the sides of the triangle.
We know that the angle ACD = 30.
Assuming CD as the base (b), we can say that CD (h) = \(\sqrt{3}\) AD

Area of the triangle = (1/2)*b*h = \(2 \sqrt{3}\)
Hence we can find the value of b = \(2 \sqrt{3}\)

CD is a part of the triangle that is isosceles (two angles are same - this means two sides will be same)
Hence CD = DE (the side of the square)

Area of the square = DE*DE = \(2 \sqrt{3}\)*\(2 \sqrt{3}\) =12
Option E


A 30-60-90 right angled triangle has ratio of sides as 1:sq rt 3 : 2
How did you reach to value of CD (h) = √3 AD ? [ Please explain why AD is being multiplied in √3 AD?]
User avatar
B
acegmat123
Manager
Manager
Joined: 28 Jun 2016
Posts: 153
Own Kudos [?]: 190 [0]
Given Kudos: 99
Location: Canada
Concentration: Operations, Entrepreneurship
Send PM
Re: If the area of Rectangle ABCD is 4√3, then what is the area of the [#permalink] New post   22 Oct 2016, 15:09
Manonamission wrote:
OptimusPrepJanielle wrote:
amithyarli wrote:
If the area of Rectangle ABCD is 4√3, then what is the area of the square DEFG ?

A) √3
B) 2√3
C) 4
D) 4√3
E) 12


This can be solved easily by following a systematic approach:

1. The area of the rectangle ABCD = 4 \(\sqrt{3}\)
Hence the area of triangle ACD would be half = \(2 \sqrt{3}\)

Now, we need to find the sides of the triangle.
We know that the angle ACD = 30.
Assuming CD as the base (b), we can say that CD (h) = \(\sqrt{3}\) AD

Area of the triangle = (1/2)*b*h = \(2 \sqrt{3}\)
Hence we can find the value of b = \(2 \sqrt{3}\)

CD is a part of the triangle that is isosceles (two angles are same - this means two sides will be same)
Hence CD = DE (the side of the square)

Area of the square = DE*DE = \(2 \sqrt{3}\)*\(2 \sqrt{3}\) =12
Option E


A 30-60-90 right angled triangle has ratio of sides as 1:sq rt 3 : 2
How did you reach to value of CD (h) = √3 AD ? [ Please explain why AD is being multiplied in √3 AD?]




A right triangle with 30-60-90 can be written as

a : a*sqrt(3) : 2a

Where 'a' is the side of the smallest length which is opposite to 30 degree

Area of rectangle ABCD = a*a*sqrt(3) = 4*sqrt(3)

Therefore a=2

CD=2*sqrt(3)= DE

Area of square = (2*sqrt(3))^2 = 12


Sent from my iPhone using GMAT Club Forum mobile app
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32681
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: If the area of Rectangle ABCD is 43, then what is the area of the [#permalink] New post   08 Nov 2022, 06:12
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 Club Bot
gmatclubot
Re: If the area of Rectangle ABCD is 43, then what is the area of the [#permalink]
08 Nov 2022, 06:12
Moderators:
Bunuel
Math Expert
92915 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions