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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] New post 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 24 Sep 2012, 10:28, edited 1 time in total.
Renamed the topic and edited the question.
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Re: what is the perimeter of the garden, in feet? [#permalink] New post 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.


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
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Re: what is the perimeter of the garden, in feet? [#permalink] New post 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] New post 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.

Answer: B.
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Re: what is the perimeter of the garden, in feet? [#permalink] 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".
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Re: what is the perimeter of the garden, in feet? [#permalink] 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.
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Re: what is the perimeter of the garden, in feet? [#permalink] 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?
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Re: what is the perimeter of the garden, in feet? [#permalink] New post 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] 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
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Re: The area of a square garden is A square feet and the perimet [#permalink] 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..
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Re: The area of a square garden is A square feet and the perimet [#permalink] New post 13 Nov 2013, 13:42
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Re: The area of a square garden is A square feet and the perimet   [#permalink] 13 Nov 2013, 13:42
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