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

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Manager
Joined: 08 Feb 2006
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The area of a square garden is A square feet and the perimet [#permalink]

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19 Apr 2006, 21:50
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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-area-of-a-square-garden-is-a-square-feet-and-the-perimet-93425.html
[Reveal] Spoiler: OA

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Director
Joined: 04 Jan 2006
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19 Apr 2006, 21:53
B...

A = P^2/4
A = 2P+9
2 equations...
solve for P...

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Manager
Joined: 20 Mar 2005
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Location: Colombia, South America

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19 Apr 2006, 21:55
jlui4477 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

I think backsolving is the easiest for this one

as A must be a square
then 2P+9 must be a square
it happens to be 36
as 36*2 + 9 = 81

so I would go with B

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VP
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20 Apr 2006, 07:06

p^2 - 36P + 4P - 144 =0

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

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21 May 2014, 10:38
Perimeter of square = P
Side of square = P/4

Area of Square = (P^2)/16 =A

Given that A = 2P + 9

(P^2)/16 = 2P + 9

P^2 = 32P + 144

P^2 -32P -144 = 0

P^2 -36P + 4P -144 = 0

P(P-36)+4(P+36) = 0

(P-36)(P+4) = 0

P = 36 o r- 4

Discarding negative value , P = 36

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Intern
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Location: India
Schools: IIMC
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Re: The area of a square garden is A square feet and the [#permalink]

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22 May 2014, 02:02
Using Hit and Trial:

Regards,
Rajat
Attachments

Post 8_Area&Perimeter.png [ 32.88 KiB | Viewed 1553 times ]

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

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22 May 2014, 02:31
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 $$x=9$$ --> $$perimeter=p=4x=36$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-area-of-a-square-garden-is-a-square-feet-and-the-perimet-93425.html
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Kudos [?]: 133166 [0], given: 12419

Re: The area of a square garden is A square feet and the perimet   [#permalink] 22 May 2014, 02:31
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