The area of a square garden is A square feet and the perimet : GMAT Problem Solving (PS)
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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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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".
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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, 09:46
Solving it using the options is probably the fastest. Especially once you figure out that the side of the square is Odd.
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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, 12:46
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?
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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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Re: The area of a square garden is A square feet and the perimet [#permalink]

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

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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..
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13 Nov 2013, 13:42
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19 Nov 2014, 06:26
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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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!
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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, 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" .
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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, 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
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Current Student Joined: 03 Oct 2014 Posts: 145 Location: India Concentration: Operations, Technology GMAT 1: 720 Q48 V40 WE: Engineering (Aerospace and Defense) Followers: 2 Kudos [?]: 29 [0], given: 89 Re: The area of a square garden is A square feet and the perimet [#permalink] ### Show Tags 26 Jan 2015, 22:23 Substitute....area - s^2.....p - 4s......side = 9...Perimeter comes out to be 36 Manager Joined: 27 Jun 2014 Posts: 78 Location: New Zealand Concentration: Strategy, General Management GMAT 1: 710 Q43 V45 GRE 1: 324 Q161 V163 GRE 2: 325 Q159 V166 GPA: 3.6 WE: Editorial and Writing (Computer Software) Followers: 4 Kudos [?]: 44 [0], given: 125 Re: The area of a square garden is A square feet and the perimet [#permalink] ### Show Tags 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. _________________ "Hardwork is the easiest way to success." - Aviram One more shot at the GMAT...aiming for a more balanced score. GMAT Club Legend Joined: 09 Sep 2013 Posts: 13435 Followers: 575 Kudos [?]: 163 [0], given: 0 Re: The area of a square garden is A square feet and the perimet [#permalink] ### Show Tags 30 Jan 2016, 09:11 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. _________________ Intern Joined: 01 Jan 2016 Posts: 5 Followers: 0 Kudos [?]: 1 [0], given: 85 Re: The area of a square garden is A square feet and the perimet [#permalink] ### Show Tags 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 Joined: 16 Oct 2010 Posts: 7119 Location: Pune, India Followers: 2132 Kudos [?]: 13633 [1] , given: 222 Re: The area of a square garden is A square feet and the perimet [#permalink] ### Show Tags 02 May 2016, 17:33 1 This post received KUDOS Expert's post 1 This post was BOOKMARKED 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 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] 02 May 2016, 17:33

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