It is currently 14 Dec 2017, 05:29

Decision(s) Day!:

CHAT Rooms | Wharton R1 | Stanford R1 | Tuck R1 | Ross R1 | Haas R1


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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

An equilateral triangle and three squares are combined as shown above,

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42606

Kudos [?]: 135613 [2], given: 12705

An equilateral triangle and three squares are combined as shown above, [#permalink]

Show Tags

New post 20 Sep 2016, 07:41
2
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

72% (01:43) correct 28% (01:57) wrong based on 129 sessions

HideShow timer Statistics

Image
An equilateral triangle and three squares are combined as shown above, forming a shape of area 48+4√3. What is the perimeter of the shape formed by the triangle and squares?

A. 18
B. 27
C. 36
D. 48
E. 64

[Reveal] Spoiler:
Attachment:
T6027.png
T6027.png [ 5.85 KiB | Viewed 1661 times ]
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135613 [2], given: 12705

Manager
Manager
avatar
B
Joined: 24 Oct 2013
Posts: 150

Kudos [?]: 22 [0], given: 129

Location: India
Concentration: General Management, Strategy
WE: Information Technology (Computer Software)
Re: An equilateral triangle and three squares are combined as shown above, [#permalink]

Show Tags

New post 20 Sep 2016, 09:16
triangle area = root(3)s^2/4
area of 3 squares together = 3 s^2

root(3)s^2/4 + 3 s^2 = 48 +4root(3)
root(3)/4s^2 = 4root(3)

s^2 = 16 => s = 4

there are 3 sides of each square = 3(4)(3) = 36

Option C

Kudos [?]: 22 [0], given: 129

Retired Moderator
avatar
G
Joined: 26 Nov 2012
Posts: 594

Kudos [?]: 181 [0], given: 45

Premium Member CAT Tests
An equilateral triangle and three squares are combined as shown above, [#permalink]

Show Tags

New post 20 Sep 2016, 12:39
Bunuel wrote:
Image
An equilateral triangle and three squares are combined as shown above, forming a shape of area 48+4√3. What is the perimeter of the shape formed by the triangle and squares?

A. 18
B. 27
C. 36
D. 48
E. 64

[Reveal] Spoiler:
Attachment:
T6027.png


We are given three square and equilateral triangle areas combines is 48+4√3.

Now we can write as \(3a^2\) + √3/4( \(a^2\) ) = 48+4√3.

=> \(a^2\) ( 3 + √3/4) = 4(12+√3)

=> \(a^2\) ( (12+√3/4) ) = 4(12+√3)
=> \(a^2\) (1/4) = 4
=> \(a^2\) = 16
a = 4.

We need to take only external sides of the figures , overall we have 9 sides of equal length , we get 9*4 = 36

IMO option C.

Kudos [?]: 181 [0], given: 45

Manager
Manager
avatar
Joined: 11 Jul 2016
Posts: 81

Kudos [?]: 33 [0], given: 87

Re: An equilateral triangle and three squares are combined as shown above, [#permalink]

Show Tags

New post 22 Oct 2016, 23:34
The Q is formula based

Total area of square and triangle = ( 3+sq rt3/4) * Side^2

( 3+sq rt3/4) * Side^2 = 48 +4 sq rt3

=> Side^2 = 16
=>Side = 4

Perimeter is sum of external sides = 9 * 4 = 36 C

Kudos [?]: 33 [0], given: 87

Board of Directors
User avatar
G
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3111

Kudos [?]: 1146 [0], given: 327

Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: An equilateral triangle and three squares are combined as shown above, [#permalink]

Show Tags

New post 23 Oct 2016, 00:45
1
This post was
BOOKMARKED
Bunuel wrote:
Image
An equilateral triangle and three squares are combined as shown above, forming a shape of area 48+4√3. What is the perimeter of the shape formed by the triangle and squares?

A. 18
B. 27
C. 36
D. 48
E. 64

[Reveal] Spoiler:
Attachment:
The attachment T6027.png is no longer available


Attachment:
T6027.png
T6027.png [ 7.17 KiB | Viewed 1007 times ]


There are 4 shapes -

1. 3 Squares of sides a
2. 1 Triangle of side a

Area of 3 Squares = \(3*a^2\)

Area of Triangle = \(\frac{√3}{4}a^2\)

Now, \(\frac{√3}{4}a^2\) + \(3a^2\) = \(48+4√3\)

Or, \(a^2(\frac{√3}{4}\) + \(3 )\) = \(48+4√3\)

Or, \(a^2( √3\) + \(12)\) = \(4 ( 48+4√3 )\)

Or, \(a^2( √3\) + \(12)\) = \(192 + 16√3\)

Or, \(a^2 = 16\)

Or, \(a = 4\)

Quote:
What is the perimeter of the shape formed by the triangle and squares?


Count the number of sides in the figure = 9

So, Perimeter is \(9*4 = 36\)

Hence answer will be (C)
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Kudos [?]: 1146 [0], given: 327

1 KUDOS received
VP
VP
avatar
P
Joined: 22 May 2016
Posts: 1126

Kudos [?]: 402 [1], given: 645

Re: An equilateral triangle and three squares are combined as shown above, [#permalink]

Show Tags

New post 25 Nov 2017, 08:23
1
This post received
KUDOS
1
This post was
BOOKMARKED
Bunuel wrote:
Image
An equilateral triangle and three squares are combined as shown above, forming a shape of area 48+4√3. What is the perimeter of the shape formed by the triangle and squares?

A. 18
B. 27
C. 36
D. 48
E. 64

[Reveal] Spoiler:
Attachment:
The attachment T6027.png is no longer available

Quick answer

Assume the second term, \(4\sqrt{3}\), of the given area is a clue: it's likely to be the area of the equilateral triangle.
Divide 48 by 3 (squares) = 16. Square side = 4.
Check: Length = 4 must equal equilateral triangle side. Area of equilateral triangle if side = 4 is \(\frac{4^2\sqrt{3}}{4} = 4\sqrt{3}\) - Correct
Square side = 4, there are nine sides on the perimeter, 9 * 4 = 36
Answer C

Longer version

Area generally: formulas and given value

Knowing the formula for the area of an equilateral triangle makes this problem a lot easier.*

Total area = (area of three squares) + (area of equilateral triangle)

Area of three square \((3)s^2\)

Area of equilateral triangle = \(\frac{s^2\sqrt{3}}{4}\)

Total area: \(3s^2 + \frac{s^2\sqrt{3}}{4}\)

Total area = \(48 + 4√3\)

Find side length of square from area of square set equal to 48

Gamble a little. The second given term, \(4\sqrt{3}\) is likely to be the area of the equilateral triangle.
So assume that the integer portion of the given area will yield a square's side length

Set just the integer portion of the area, 48, equal to the area of the three squares

\(3s^2 = 48\)
\(s^2 = 16\)
\(s = 4\)


Check: square side = triangle side, find triangle area

Each square: has equal side lengths that are equal to the side of the equilateral triangle (each square shares a side with the triangle)
If square side length = 4, triangle side length must = 4

Set the other given term equal to the area of the equilateral triangle
\(\frac{s^2\sqrt{3}}{4} =4√3\)

\({s^2\sqrt{3}}=16√3\)

\(s^2 = 16\)
\(s = 4\)


Correct: the side of square = side of triangle = 4

Perimeter

Perimeter = 9 square side lengths: \(9 * 4 = 36\)

Answer C

*If you don't remember the formula for the area of an equilateral triangle, draw one. Drop an altitude, which is a perpendicular bisector of the opposite side and of the vertex.
That altitude creates two congruent right 30-60-90 triangles with side lengths that correspond to 30-60-90, in ratio \(x : x\sqrt{3} : 2x\)

Side lengths? Side opposite the 90° angle = \(2x = 4\). Side opposite 30° angle is half of that, i.e., \(x, x = 2\). Side opposite 60° angle = height of triangle = \(x\sqrt{3}\) or \(2\sqrt{3}\)

Area\(=\frac{b*h}{2} = (4*2\sqrt{3})*\frac{1}{2} = 4\sqrt{3}\). Correct: it is equal to the second term in the area given.

Attachment:
equitriarea.png
equitriarea.png [ 40.47 KiB | Viewed 298 times ]

Kudos [?]: 402 [1], given: 645

1 KUDOS received
Manager
Manager
User avatar
S
Status: Enjoying the Journey
Affiliations: ND
Joined: 26 Sep 2017
Posts: 83

Kudos [?]: 33 [1], given: 471

Schools: Rotman '21
WE: Marketing (Consulting)
An equilateral triangle and three squares are combined as shown above, [#permalink]

Show Tags

New post 28 Nov 2017, 00:01
1
This post received
KUDOS
genxer123 wrote:
Bunuel wrote:
Image
An equilateral triangle and three squares are combined as shown above, forming a shape of area 48+4√3. What is the perimeter of the shape formed by the triangle and squares?

A. 18
B. 27
C. 36
D. 48
E. 64

[Reveal] Spoiler:
Attachment:
T6027.png

Quick answer

Assume the second term, \(4\sqrt{3}\), of the given area is a clue: it's likely to be the area of the equilateral triangle.
Divide 48 by 3 (squares) = 16. Square side = 4.
Check: Length = 4 must equal equilateral triangle side. Area of equilateral triangle if side = 4 is \(\frac{4^2\sqrt{3}}{4} = 4\sqrt{3}\) - Correct
Square side = 4, there are nine sides on the perimeter, 9 * 4 = 36
Answer C



The quick answer is so brilliant genxer123

Thanks
_________________

"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

High achievement always takes place in the framework of high expectation Charles Kettering
If we chase perfection we can catch excellence Vince Lombardi

GMAT Club Live: 5 Principles for Fast Math: https://gmatclub.com/forum/gmat-club-live-5-principles-for-fast-math-251028.html#p1940045
YouTube sessions by GMATNinja: https://gmatclub.com/forum/verbal-live-with-gmat-ninja-sc-pronouns-that-parallelism-250568.html#p1936104
The Best SC strategies - Amazing 4 videos by Veritas: https://gmatclub.com/forum/the-best-sc-strategies-amazing-4-videos-by-veritas-250377.html#p1934575

Kudos [?]: 33 [1], given: 471

Intern
Intern
avatar
B
Joined: 26 Oct 2017
Posts: 28

Kudos [?]: 2 [0], given: 0

CAT Tests
Re: An equilateral triangle and three squares are combined as shown above, [#permalink]

Show Tags

New post 28 Nov 2017, 02:02
Perimeter is 9a.

So it's a multiple of 9.
Eliminate D, E

Now, take the hint from area (root part) and find the side of square.

So side comes out to be 4

9*4=36

C

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app

Kudos [?]: 2 [0], given: 0

Expert Post
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1940

Kudos [?]: 1018 [0], given: 3

Location: United States (CA)
Re: An equilateral triangle and three squares are combined as shown above, [#permalink]

Show Tags

New post 29 Nov 2017, 17:14
Bunuel wrote:
Image
An equilateral triangle and three squares are combined as shown above, forming a shape of area 48+4√3. What is the perimeter of the shape formed by the triangle and squares?

A. 18
B. 27
C. 36
D. 48
E. 64

[Reveal] Spoiler:
Attachment:
T6027.png


We see that the squares and the triangle have equal sides. If we let the side of either shape = n, the total area is:

(n^2√3)/4 + 3n^2 = 48+4√3

n^2√3 + 12n^2 = 192 + 16√3

Looking at the equation we see that:

n^2√3 = 16√3

And

12n^2 = 192

In either equation, we have n = 4. Thus, the perimeter is 4 x 9 = 36.

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 1018 [0], given: 3

Re: An equilateral triangle and three squares are combined as shown above,   [#permalink] 29 Nov 2017, 17:14
Display posts from previous: Sort by

An equilateral triangle and three squares are combined as shown above,

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.