GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 23 Oct 2018, 17:51

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

What is the perimeter of a regular polygon with sides of len

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

Hide Tags

Manager
Manager
User avatar
Joined: 18 Aug 2013
Posts: 107
Concentration: Entrepreneurship, Technology
GMAT 1: 740 Q48 V44
GMAT ToolKit User
What is the perimeter of a regular polygon with sides of len  [#permalink]

Show Tags

New post 12 Jun 2014, 23:39
6
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

77% (01:38) correct 23% (01:31) wrong based on 132 sessions

HideShow timer Statistics

What is the perimeter of a regular polygon with sides of length 12 cm and internal angles measuring 144° each?

A. 96 cm
B. 108 cm
C. 120 cm
D. 132 cm
E. 144 cm
Most Helpful Community Reply
Manager
Manager
avatar
Joined: 17 Nov 2013
Posts: 81
Concentration: Strategy, Healthcare
GMAT 1: 710 Q49 V38
GPA: 3.34
WE: Business Development (Health Care)
GMAT ToolKit User
Re: What is the perimeter of a regular polygon with sides of len  [#permalink]

Show Tags

New post 13 Jun 2014, 00:23
3
2
Summation of interior angles is given by:
180(N-2) = interior angle * N
N: no of sides

180(N-2) = 144N
180N - 360 = 144N
36N = 360
N = 10

Perimeter:
N * length of side = 10 * 12 = 120

C

Image Posted from GMAT ToolKit
_________________

You create your own destiny.

General Discussion
Intern
Intern
User avatar
Joined: 18 Jan 2014
Posts: 11
GMAT 1: 640 Q49 V28
GPA: 3.5
WE: Operations (Energy and Utilities)
GMAT ToolKit User Reviews Badge
Re: What is the perimeter of a regular polygon with sides of len  [#permalink]

Show Tags

New post 16 Jun 2014, 04:36
3
phlaym39 wrote:
What is the perimeter of a regular polygon with sides of length 12 cm and internal angles measuring 144° each?

A. 96 cm
B. 108 cm
C. 120 cm
D. 132 cm
E. 144 cm




Sum of all interior angles is given by:
180(n-2) = n is number of sides

180(n-2) = 144*n
from here
n = 10

So perimeter becomes 12*10= 120 answer
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1829
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: What is the perimeter of a regular polygon with sides of len  [#permalink]

Show Tags

New post 01 Oct 2014, 03:51
Interior angle = 144

Its a decagon (Polygon with 10 sides)

Formula to find sides is same as shown in above posts

Perimeter = 10 * 12 = 120

Answer = C
_________________

Kindly press "+1 Kudos" to appreciate :)

DS Forum Moderator
avatar
P
Joined: 22 Aug 2013
Posts: 1348
Location: India
Premium Member
Re: What is the perimeter of a regular polygon with sides of len  [#permalink]

Show Tags

New post 20 May 2017, 00:37
For any polygon, sum of its interior and exterior angle (at that particular vertex) = 180
If interior angle = 144, exterior angle = 180-144 = 36

For a regular polygon of n sides, each exterior angle = 360/n (sum of all exterior angles of a polygon is 360)
So 360/n = 36 or n = 10.

Perimeter of regular polygon = n* length of each side = 10*12 = 120

Hence C
Director
Director
User avatar
D
Joined: 04 Dec 2015
Posts: 701
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
GMAT ToolKit User
Re: What is the perimeter of a regular polygon with sides of len  [#permalink]

Show Tags

New post 22 May 2017, 16:40
phlaym39 wrote:
What is the perimeter of a regular polygon with sides of length 12 cm and internal angles measuring 144° each?

A. 96 cm
B. 108 cm
C. 120 cm
D. 132 cm
E. 144 cm


Let number of sides of the polygon be n. (Given its a regular polygon. Regular polygon has all sides and interior angles equal.)

Internal Angle = \(\frac{180 (n-2)}{n}\)

Given internal Angle is \(144^{\circ}\)

Therefore; \(\frac{180 (n-2)}{n}\) = \(144^{\circ}\)

180 (n-2) = 144 x n

180n - 180 x 2 = 144n

180n - 144n = 180 x 2

36n = 180 x 2

n = \(\frac{180 x 2}{36}\) = 10

Therefore total number of sides = 10.

Length of side is given = 12cm

Perimeter = 12 x 10 = 120 cm

Answer C...

_________________
Kindly press "+1 Kudos" to appreciate :)
CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 3038
Location: Canada
Re: What is the perimeter of a regular polygon with sides of len  [#permalink]

Show Tags

New post 27 Apr 2018, 06:30
Top Contributor
phlaym39 wrote:
What is the perimeter of a regular polygon with sides of length 12 cm and internal angles measuring 144° each?

A. 96 cm
B. 108 cm
C. 120 cm
D. 132 cm
E. 144 cm


Sum of ALL sides in an n-sided polygon = (n - 2)(180) degrees

So, EACH ANGLE in a regular n-sided polygon = (n - 2)(180)/n degrees

We're told that EACH ANGLE is 144°, so we can write: (n - 2)(180)/n = 144
Multiply both sides by n to get: (n - 2)(180) = 144n
Expand left side: 180n - 360 = 144n
Add 360 to both sides: 180n = 144n + 360
Subtract 144n from both sides: 36n = 360
Solve: n = 10

This tells us that the polygon has 10 sides
Since each side is the SAME LENGTH in a REGULAR polygon, the perimeter = (10)(12 cm) = 120 cm

Answer: C

Cheers,
Brent
_________________

Brent Hanneson – GMATPrepNow.com
Image
Sign up for our free Question of the Day emails

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3911
Location: United States (CA)
Re: What is the perimeter of a regular polygon with sides of len  [#permalink]

Show Tags

New post 30 Apr 2018, 16:41
phlaym39 wrote:
What is the perimeter of a regular polygon with sides of length 12 cm and internal angles measuring 144° each?

A. 96 cm
B. 108 cm
C. 120 cm
D. 132 cm
E. 144 cm


We need to determine the number of sides of this regular polygon first before we can determine its perimeter. Let’s use the formula for sum of interior angles to determine the number of angles (and thus the number of sides) of the polygon. Recall that if a polygon has n sides, the total number of degrees of the interior angles is given by 180(n - 2). Since we are given that each interior angle measures 144 degrees, the total number of degrees of the interior angles is also 144n. Thus we can create the equation:

144n = 180(n - 2)

144n = 180n - 360

360 = 36n

10 = n

Thus, the perimeter is 10 x 12 = 120.

Alternate Solution:

An exterior angle of this polygon is 180 - 144 = 36 degrees. Since exterior angles of a polygon always add up to 360, this polygon has 360 / 36 = 10 angles; which also means this polygon has 10 sides. Since each side measures 12 cm, the perimeter is 12 x 10 = 120 cm.

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

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

GMAT Club Bot
Re: What is the perimeter of a regular polygon with sides of len &nbs [#permalink] 30 Apr 2018, 16:41
Display posts from previous: Sort by

What is the perimeter of a regular polygon with sides of len

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.