GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 06 Jul 2020, 04:51

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

The area of a square garden is A square feet and the perimeter is P

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

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
Joined: 27 Feb 2010
Posts: 70
Location: Denver
The area of a square garden is A square feet and the perimeter is P  [#permalink]

Show Tags

New post Updated on: 14 Dec 2017, 00:34
3
6
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

83% (01:54) correct 17% (02:35) wrong based on 400 sessions

HideShow timer Statistics

The area of a square garden is A square feet and the perimeter is P feet. If A = 2P + 9, what is the perimeter of the garden, in feet?

A. 28
B. 36
C. 40
D. 56
E. 64

Originally posted by zz0vlb on 28 Apr 2010, 07:39.
Last edited by Bunuel on 14 Dec 2017, 00:34, edited 3 times in total.
Renamed the topic and edited the question.
Manager
Manager
avatar
Joined: 12 Jan 2010
Posts: 221
Schools: DukeTuck,Kelogg,Darden
Reviews Badge
Re: The area of a square garden is A square feet and the perimeter is P  [#permalink]

Show Tags

New post 28 Apr 2010, 07:44
3
1
zz0vlb wrote:
The area of a square garden is A square feet and the perimeter is P feet. If A=2P+9 what is the perimeter of the garden, in feet?

a.28
b.36
c.40
d.56
e.64

these type problems are similar to finding a tiny gray spot on a black paper.


IMO Answer is b. 36.

Let side be a
P = 4a
A = a^2

Sub in equation A=2P+9

a^2 = 8a +9
a^2-8a +9 = 0
a = 9 or -1

So P = 4*9 = 36.

Hope this helps
Retired Moderator
User avatar
Status: The last round
Joined: 18 Jun 2009
Posts: 1133
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
GMAT ToolKit User
Re: The area of a square garden is A square feet and the perimeter is P  [#permalink]

Show Tags

New post 28 Apr 2010, 07:47
\(A=l * l =l^2\)

\(P= 4l\)

Hence, \(l^2=2*4l+9\)
Solving \(l\) will give two values, \(l=-1\) or \(l=9\) as \(l\) cant be negative so \(l=9\)

\(P=4*9=36\)

So "B".
_________________
Manager
Manager
avatar
Joined: 12 Jan 2010
Posts: 221
Schools: DukeTuck,Kelogg,Darden
Reviews Badge
Re: The area of a square garden is A square feet and the perimeter is P  [#permalink]

Show Tags

New post 28 Apr 2010, 09:46
Solving it using the options is probably the fastest. Especially once you figure out that the side of the square is Odd.
Intern
Intern
avatar
Joined: 28 Apr 2010
Posts: 2
Re: The area of a square garden is A square feet and the perimeter is P  [#permalink]

Show Tags

New post 28 Apr 2010, 12:46
Silvers wrote:
Solving it using the options is probably the fastest. Especially once you figure out that the side of the square is Odd.



How did you figure that out that its odd?
Manager
Manager
avatar
Joined: 12 Jan 2010
Posts: 221
Schools: DukeTuck,Kelogg,Darden
Reviews Badge
Re: The area of a square garden is A square feet and the perimeter is P  [#permalink]

Show Tags

New post 28 Apr 2010, 12:48
1
gxsingh wrote:
Silvers wrote:
Solving it using the options is probably the fastest. Especially once you figure out that the side of the square is Odd.



How did you figure that out that its odd?


Oh Thats Simple, equation says

A = 2P + 9

So means area is Odd so side is the square root of the area and has to be odd.

hope this helps :)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64992
The area of a square garden is A square feet and the perimeter is P  [#permalink]

Show Tags

New post 24 Sep 2012, 10:30
2
zz0vlb wrote:
The area of a square garden is A square feet and the perimeter is P feet. If A = 2P + 9, what is the perimeter of the garden, in feet?

A. 28
B. 36
C. 40
D. 56
E. 64


Let the side of garden be \(x\) feet, then: \(area=a=x^2\) and \(perimeter=p=4x\).

Given: \(a=2p+9\) --> \(x^2=2*4x+9\) --> solving for \(x\): \(x=-1\) (not a valid solution as \(x\) represents the length and therefore must be positive) or \(x=9\) --> \(perimeter=p=4x=36\).

Answer: B.
_________________
Manager
Manager
avatar
B
Joined: 02 Nov 2009
Posts: 94
Re: The area of a square garden is A square feet and the perimeter is P  [#permalink]

Show Tags

New post 28 Sep 2012, 20:23
This is hovv i solved it

A = a^2 it is a square implies it should be a perfect square

If A = 2P+9, implies a^2 = 2p+9

a^2 = 2(28) + 9 not a perfect square
a^2 = 2(36) + 9 perfect square = 80 so a = 9 so permieter = 36 true B
a^2 = 2(40) + 9 not a perfect square
a^2 = 2(56) + 9 perfect square = 121 so a = 11 if a =11 then permiter =44 condition fails
a^2 = 2(64) + 9 not a perfect square
Senior Manager
Senior Manager
avatar
Joined: 06 Aug 2011
Posts: 309
Re: The area of a square garden is A square feet and the perimeter is P  [#permalink]

Show Tags

New post 28 Sep 2012, 21:17
Area===== assume it L2.. because..L*L area..

permiter=========4L

a=2p+9...

L2=2(4L)+9.

L2-8L-9=0

L will contain two solutions.. L=-1 or +9..

-1 can not be the Length or anyside..so its 9..9*4..=36..
_________________
Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !
Senior Manager
Senior Manager
User avatar
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 393
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: The area of a square garden is A square feet and the perimeter is P  [#permalink]

Show Tags

New post 11 Jan 2015, 04:21
Hey,

This is a fairly easy problem, but I think the stem is not very clear. That because it says a=2p+9, but it doesn't clarify if this "a" is the area. Especially since before it was stated that the area is A. At least I was left wondering is "a" is the area of the side of the square.

Anyway, I did it both ways. It didn't work out as "a" being the side, so I concluded that it must be the area. And I know that it doesn't make much sense to be the side, since "p", the perimeter, cannot be less than the side. Still though I think it is not clear enough!
Intern
Intern
avatar
B
Joined: 23 Dec 2014
Posts: 47
Re: The area of a square garden is A square feet and the perimeter is P  [#permalink]

Show Tags

New post 26 Jan 2015, 16:45
pacifist85 wrote:
Hey,

This is a fairly easy problem, but I think the stem is not very clear. That because it says a=2p+9, but it doesn't clarify if this "a" is the area. Especially since before it was stated that the area is A. At least I was left wondering is "a" is the area of the side of the square.

Anyway, I did it both ways. It didn't work out as "a" being the side, so I concluded that it must be the area. And I know that it doesn't make much sense to be the side, since "p", the perimeter, cannot be less than the side. Still though I think it is not clear enough!


I was thinking the same question. He said "a" not "A" .
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 10634
Location: Pune, India
Re: The area of a square garden is A square feet and the perimeter is P  [#permalink]

Show Tags

New post 26 Jan 2015, 21:30
Salvetor wrote:
pacifist85 wrote:
Hey,

This is a fairly easy problem, but I think the stem is not very clear. That because it says a=2p+9, but it doesn't clarify if this "a" is the area. Especially since before it was stated that the area is A. At least I was left wondering is "a" is the area of the side of the square.

Anyway, I did it both ways. It didn't work out as "a" being the side, so I concluded that it must be the area. And I know that it doesn't make much sense to be the side, since "p", the perimeter, cannot be less than the side. Still though I think it is not clear enough!


I was thinking the same question. He said "a" not "A" .


Yes, the area is given as 'A' and perimeter as 'P' and the relation between them is given as A = 2P + 9
The different As seem to be a typing oversight.

You need to find the perimeter so get rid of A. Side of the square will be \(\sqrt{A}\).
So Perimeter \(P = 4*Side = 4\sqrt{A}\)
\(A = P^2/16 = 2P + 9\)
Solving, we get P = 36
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern
Intern
avatar
G
Joined: 01 Jan 2016
Posts: 28
CAT Tests
Re: The area of a square garden is A square feet and the perimeter is P  [#permalink]

Show Tags

New post 02 May 2016, 17:08
VeritasPrepKarishma wrote:
Salvetor wrote:
pacifist85 wrote:
Hey,

This is a fairly easy problem, but I think the stem is not very clear. That because it says a=2p+9, but it doesn't clarify if this "a" is the area. Especially since before it was stated that the area is A. At least I was left wondering is "a" is the area of the side of the square.

Anyway, I did it both ways. It didn't work out as "a" being the side, so I concluded that it must be the area. And I know that it doesn't make much sense to be the side, since "p", the perimeter, cannot be less than the side. Still though I think it is not clear enough!


I was thinking the same question. He said "a" not "A" .


Yes, the area is given as 'A' and perimeter as 'P' and the relation between them is given as A = 2P + 9
The different As seem to be a typing oversight.

You need to find the perimeter so get rid of A. Side of the square will be \(\sqrt{A}\).
So Perimeter \(P = 4*Side = 4\sqrt{A}\)
\(A = P^2/16 = 2P + 9\)
Solving, we get P = 36



I used this method,but end up with a complex quadratic equation - P^2-32P-144=0 Any quick ways to solve for p from that quadratic equation?
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 10634
Location: Pune, India
Re: The area of a square garden is A square feet and the perimeter is P  [#permalink]

Show Tags

New post 02 May 2016, 17:33
1
theperfectgentleman wrote:

I used this method,but end up with a complex quadratic equation - P^2-32P-144=0 Any quick ways to solve for p from that quadratic equation?


Note that the equation has negative coefficient of P and a negative constant term.
So sum of roots and product of roots both are negative. Hence one root is negative and the other positive. So at least one root will be greater than 32. Since the product of both is 144, the other root will be very small such as 2, 3 or 4. You see that 36*4 = 144 so you get the split as

P^2 - 36P + 4P - 144 = 0
(P - 36)(P + 4) = 0
P = 36
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager
Manager
User avatar
S
Joined: 17 Nov 2014
Posts: 57
Location: India
Re: The area of a square garden is A square feet and the perimeter is P  [#permalink]

Show Tags

New post 03 May 2016, 07:07
Let side be a
P = 4a
A = a^2

Sub in equation A=2P+9

a^2 = 8a +9
a^2-8a +9 = 0
a = 9 or -1

So P = 4*9 = 36.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15387
Re: The area of a square garden is A square feet and the  [#permalink]

Show Tags

New post 15 Oct 2019, 02:27
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.
_________________
GMAT Club Bot
Re: The area of a square garden is A square feet and the   [#permalink] 15 Oct 2019, 02:27

The area of a square garden is A square feet and the perimeter is P

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





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