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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # The area of a square garden is A square feet and the perimeter is P

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

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3
6 00:00

Difficulty:   5% (low)

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

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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

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  Joined: 12 Jan 2010
Posts: 221
Schools: DukeTuck,Kelogg,Darden
Re: The area of a square garden is A square feet and the perimeter is P  [#permalink]

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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.

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 perimeter is P  [#permalink]

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$$A=l * l =l^2$$

$$P= 4l$$

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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Manager  Joined: 12 Jan 2010
Posts: 221
Schools: DukeTuck,Kelogg,Darden
Re: The area of a square garden is A square feet and the perimeter is P  [#permalink]

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

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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: 12 Jan 2010
Posts: 221
Schools: DukeTuck,Kelogg,Darden
Re: The area of a square garden is A square feet and the perimeter is P  [#permalink]

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

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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 $$x=9$$ --> $$perimeter=p=4x=36$$.

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

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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: 309
Re: The area of a square garden is A square feet and the perimeter is P  [#permalink]

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

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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  B
Joined: 23 Dec 2014
Posts: 47
Re: The area of a square garden is A square feet and the perimeter is P  [#permalink]

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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 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]

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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

Intern  G
Joined: 01 Jan 2016
Posts: 28
Re: The area of a square garden is A square feet and the perimeter is P  [#permalink]

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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 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]

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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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Karishma
Veritas Prep GMAT Instructor

Manager  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]

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

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_________________ 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  