If the perimeter of square region S and the perimeter of rec : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 19 Jan 2017, 12:21

### 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 perimeter of square region S and the perimeter of rec

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: D-Day is on February 10th. and I am not stressed
Affiliations: American Management association, American Association of financial accountants
Joined: 12 Apr 2011
Posts: 270
Location: Kuwait
Schools: Columbia university
Followers: 5

Kudos [?]: 272 [3] , given: 52

If the perimeter of square region S and the perimeter of rec [#permalink]

### Show Tags

03 Feb 2012, 07:21
3
KUDOS
17
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

78% (02:36) correct 22% (02:01) wrong based on 502 sessions

### HideShow timer Statistics

If the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of S

A. 25:16
B. 24:25
C. 5:6
D. 4:5
E. 4:9
[Reveal] Spoiler: OA

_________________

Sky is the limit

Math Expert
Joined: 02 Sep 2009
Posts: 36567
Followers: 7081

Kudos [?]: 93194 [2] , given: 10553

Re: the primeters of square and rectangle [#permalink]

### Show Tags

03 Feb 2012, 07:29
2
KUDOS
Expert's post
8
This post was
BOOKMARKED
If the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of S
A. 25:16
B. 24:25
C. 5:6
D. 4:5
E. 4:9

Let the side of square be $$s$$ and the side of rectangle $$a$$ and $$b$$

Given: $$\frac{a}{b}=\frac{2}{3}$$ --> $$b=\frac{3a}{2}$$. Also: $$P=4s=2(a+b)$$ --> $$2s=a+b=\frac{5a}{2}$$ --> $$s=\frac{5a}{4}$$.
Question: $$\frac{ab}{s^2}=?$$

$$\frac{ab}{s^2}=\frac{3a^2}{2}*\frac{16}{25a^2}=\frac{24}{25}$$.

OR: you can pick numbers: let the sides of rectangle be 4 and 6 (ratio 2:3) then the perimeter of the rectangle will be 2(4+6)=20, thus the side of the square will be 20/4=5. Next, the area of the rectangle will be 4*6=24 and the area of the square will be 5^2=25, so the ratio of the areas will be 24/25.

OR: if we take the side of rectangle to be 2x and 3x (for some positive multiple x), then the perimeter of the rectangle will be 2(2x+3x)=10x, thus the side of the square will be 10x/4=5x/2. Next, the area of the rectangle will be 2x*3x=6x^2 and the area of the square will be (5x/2)^2=25x^2/4, so the ratio of the areas will be 24/25.

_________________
Senior Manager
Status: D-Day is on February 10th. and I am not stressed
Affiliations: American Management association, American Association of financial accountants
Joined: 12 Apr 2011
Posts: 270
Location: Kuwait
Schools: Columbia university
Followers: 5

Kudos [?]: 272 [0], given: 52

Re: If the perimeter of square region S and the perimeter of rec [#permalink]

### Show Tags

03 Feb 2012, 09:17
GOT IT, 2ND APPROACH IS EASIER...THAAAAAANKS B.
_________________

Sky is the limit

Math Expert
Joined: 02 Sep 2009
Posts: 36567
Followers: 7081

Kudos [?]: 93194 [0], given: 10553

Re: If the perimeter of square region S and the perimeter of rec [#permalink]

### Show Tags

20 Jun 2013, 05:39
Expert's post
1
This post was
BOOKMARKED
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

_________________
Intern
Joined: 15 Jun 2013
Posts: 7
Concentration: Strategy, Finance
GMAT Date: 02-13-2014
Followers: 0

Kudos [?]: 6 [0], given: 6

Re: If the perimeter of square region S and the perimeter of rec [#permalink]

### Show Tags

24 Sep 2013, 00:59
manalq8 wrote:
If the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of S
A. 25:16
B. 24:25
C. 5:6
D. 4:5
E. 4:9

We know Perimeter of a square (Ps) = 4*side
Perimeter of a rectangle (Pr) = 2(length+breath)

Let us assume 40 to be the perimeter of the square (since we know each side of a square is equal and the perimeter is divisible by 4, also take in to account the length and breadth of the rectangle is in the ration 2k:3k = 5k; we can assume such a number)

Therefore,
Ps = Pr = 40
Area of the square = 100 sq. units
i.e. length + breadth = 20 (or 5k = 20 given that l:b (or b:l) = 2:3)
Therefore length = 8, breath = 12

Area of the rectangle = 8*12 = 96 sq. units

Question asked = Area of the rectangle : Area of the square = 96:100 ==> 24:25

Note : The explanation might be bigger, but it takes less than 15 seconds to solve this problem if you assume numbers and try the problem.
Intern
Joined: 09 Jul 2014
Posts: 44
Followers: 0

Kudos [?]: 2 [0], given: 63

Re: If the perimeter of square region S and the perimeter of rec [#permalink]

### Show Tags

06 Oct 2014, 08:30
Bunuel has given a pretty good explanation. But still,, here is how i approached it :
For rectangle of length a and Breadth b: given is a/b = 2/3 ie a =2x/5 and b=3x/5(where x is some multiplication factor of the ratio). So, Perimeter of R = 2(a+b) = 2(2x/5 + 3x/5) = 2x
Perimeter of S = 4Side = 2x Therefore Side = x/2.
Area R (a*b):Area S side^2 = 6x^2/25 / x^2/4 = 24:25 .

Hope i could help
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13456
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: If the perimeter of square region S and the perimeter of rec [#permalink]

### Show Tags

17 Oct 2015, 07:06
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 Legend
Joined: 09 Sep 2013
Posts: 13456
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: If the perimeter of square region S and the perimeter of rec [#permalink]

### Show Tags

02 Nov 2016, 07:20
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.
_________________
Math Forum Moderator
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 2302
Location: India
GPA: 3.5
Followers: 92

Kudos [?]: 633 [0], given: 317

Re: If the perimeter of square region S and the perimeter of rec [#permalink]

### Show Tags

02 Nov 2016, 07:57
manalq8 wrote:
If the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of S

A. 25:16
B. 24:25
C. 5:6
D. 4:5
E. 4:9

In figure R -

Length = 3 ; Breadth = 2

Area of R = 6 and Perimeter of R = 2 ( 3 + 2 ) => 10

In figure S -

Sides = S (Say)

So, 4s = 10

Or, s = 5/2

Area of S = 25/4

Hence area of R to the area of S = 6 : 25/4 => 24 : 25

Hence, Correct answer will be (B) 24: 25
_________________

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 )

Re: If the perimeter of square region S and the perimeter of rec   [#permalink] 02 Nov 2016, 07:57
Similar topics Replies Last post
Similar
Topics:
10 The perimeter of square S is 40. 11 08 Feb 2014, 05:55
3 If the perimeter of square region S and the perimeter of 9 07 Sep 2010, 12:01
11 If the perimeter of square region S and the perimeter of the 9 19 Jun 2010, 21:23
15 The area of a square garden is A square feet and the perimet 20 28 Apr 2010, 07:39
1 What is the area of a square with perimeter P ? 2 01 Jun 2007, 20:13
Display posts from previous: Sort by