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# The area of a square garden is A square feet and the perimet

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The area of a square garden is A square feet and the perimet [#permalink]

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28 Apr 2010, 07:39
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Jan 2015, 04:33, edited 2 times in total.
Renamed the topic and edited the question.
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28 Apr 2010, 07:44
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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.

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
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Re: The area of a square garden is A square feet and the perimet [#permalink]

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24 Sep 2012, 10:30
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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 $$x=9$$ --> $$perimeter=p=4x=36$$.

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Re: The area of a square garden is A square feet and the perimet [#permalink]

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28 Apr 2010, 12:48
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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
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02 May 2016, 17:33
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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
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Retired Moderator Status: The last round Joined: 18 Jun 2009 Posts: 1310 Concentration: Strategy, General Management GMAT 1: 680 Q48 V34 Followers: 79 Kudos [?]: 1005 [0], given: 157 Re: The area of a square garden is A square feet and the perimet [#permalink] ### Show Tags 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". _________________ Senior Manager Joined: 12 Jan 2010 Posts: 257 Schools: DukeTuck,Kelogg,Darden Followers: 6 Kudos [?]: 78 [0], given: 28 Re: The area of a square garden is A square feet and the perimet [#permalink] ### Show Tags 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. _________________ Run towards the things that make you uncomfortable daily. The greatest risk is not taking risks http://gmatclub.com/forum/from-690-to-730-q50-v38-97356.html Intern Joined: 28 Apr 2010 Posts: 2 Followers: 0 Kudos [?]: 0 [0], given: 8 Re: The area of a square garden is A square feet and the perimet [#permalink] ### Show Tags 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 Joined: 25 Jun 2012 Posts: 71 Location: India WE: General Management (Energy and Utilities) Followers: 4 Kudos [?]: 107 [0], given: 15 Re: The area of a square garden is A square feet and the perimet [#permalink] ### Show Tags 24 Sep 2012, 10:24 Silvers wrote: 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 Silvers, I still dont understand the statement here....can u pls give an example? Manager Joined: 02 Nov 2009 Posts: 138 Followers: 3 Kudos [?]: 165 [0], given: 97 Re: The area of a square garden is A square feet and the perimet [#permalink] ### Show Tags 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 Joined: 06 Aug 2011 Posts: 405 Followers: 2 Kudos [?]: 192 [0], given: 82 Re: The area of a square garden is A square feet and the perimet [#permalink] ### Show Tags 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 ! GMAT Club Legend Joined: 09 Sep 2013 Posts: 13497 Followers: 577 Kudos [?]: 163 [0], given: 0 Re: The area of a square garden is A square feet and the perimet [#permalink] ### Show Tags 13 Nov 2013, 13:42 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: 13497 Followers: 577 Kudos [?]: 163 [0], given: 0 Re: The area of a square garden is A square feet and the perimet [#permalink] ### Show Tags 19 Nov 2014, 06:26 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. _________________ Senior Manager Status: Math is psycho-logical Joined: 07 Apr 2014 Posts: 443 Location: Netherlands GMAT Date: 02-11-2015 WE: Psychology and Counseling (Other) Followers: 2 Kudos [?]: 109 [0], given: 169 Re: The area of a square garden is A square feet and the perimet [#permalink] ### Show Tags 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! Manager Joined: 23 Dec 2014 Posts: 51 Followers: 0 Kudos [?]: 5 [0], given: 53 Re: The area of a square garden is A square feet and the perimet [#permalink] ### Show Tags 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 Joined: 16 Oct 2010 Posts: 7125 Location: Pune, India Followers: 2138 Kudos [?]: 13691 [0], given: 222 Re: The area of a square garden is A square feet and the perimet [#permalink] ### Show Tags 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 My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: The area of a square garden is A square feet and the perimet [#permalink]

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26 Jan 2015, 22:23
Substitute....area - s^2.....p - 4s......side = 9...Perimeter comes out to be 36
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Re: The area of a square garden is A square feet and the perimet [#permalink]

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29 Jan 2015, 18:46
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

Please edit question to read A= 2p+9. a is different from A and I spent 10 minutes scratching my head over this typo.
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30 Jan 2016, 09:11
Hello from the GMAT Club BumpBot!

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Re: The area of a square garden is A square feet and the perimet [#permalink]

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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?
Re: The area of a square garden is A square feet and the perimet   [#permalink] 02 May 2016, 17:08

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