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

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Manager
Joined: 09 Jun 2010
Posts: 63
The area of a square garden is A square feet and the  [#permalink]

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25 Jul 2010, 23:56
00:00

Difficulty:

5% (low)

Question Stats:

97% (02:18) correct 3% (02:05) wrong based on 51 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/the-area-of- ... 93425.html
Manager
Joined: 16 Apr 2010
Posts: 199
Re: The area of a square garden is A square feet and the  [#permalink]

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26 Jul 2010, 00:39
1
Hi,

The perimeter of the square is 4*length of one side.
The area of the square = Side*Side

Let x = side of the square
a = 2p+9
x*x = 2(x/4) +9
x*x - x/2 - 9 = 0
Solve for x and the area is x*x.

regards,
Jack
Math Expert
Joined: 02 Sep 2009
Posts: 53020
Re: The area of a square garden is A square feet and the  [#permalink]

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26 Jul 2010, 00:49
1
xmagedo 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?
28
36
40
56
64

thanks
tell me about the formula !

The above solution is not right.

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

_________________
Manager
Joined: 09 Jun 2010
Posts: 63
Re: The area of a square garden is A square feet and the  [#permalink]

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26 Jul 2010, 00:54
Pleas can you explain how x=9 ? I didnt get this point
thanks
Math Expert
Joined: 02 Sep 2009
Posts: 53020
Re: The area of a square garden is A square feet and the  [#permalink]

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26 Jul 2010, 01:30
xmagedo wrote:
Pleas can you explain how x=9 ? I didnt get this point
thanks

You'll have quadratic equation $$x^2-8x-9=0$$ and you should solve it for $$x$$ --> $$x=-1$$ or $$x=9$$.
_________________
Senior Manager
Joined: 18 Sep 2009
Posts: 273
Re: The area of a square garden is A square feet and the  [#permalink]

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26 Jul 2010, 17:24
If side = s
A=s*s
P= 4s
A = 2(p)+9
= 2(4s)+9
= 8s +9
s*s = 8s+9
s*s-8s-9=0
s*s-9s+s-9=0
s(s-9)+1(s-9)=0
(s-9) (s+1)=0
s=9 or -1
s=9
P=4(s) = 4(9)=36
Intern
Joined: 22 Jun 2010
Posts: 48
Re: The area of a square garden is A square feet and the  [#permalink]

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27 Jul 2010, 02:42
xmagedo 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?
28
36
40
56
64

thanks
tell me about the formula !

You can also solve this via using the given numbers in the answer choices!

Of course you need to be aware of the basic properties as outlined by the other posts above (a = x^2 and p = 4x)

Starting with D you will notice that x=14 is way too big for your area (14^2) and will not satisfy: a=2p+9

--> Eliminate D and E

Now pick B (its either too big, then its A, or too small then you know its C or it is B itsself)

And picking B indeed solves the problem! (36/4 --> 9; a= 9^2 = 81 and 81=2x36+9)

Cheers,
André
Director
Joined: 03 Sep 2006
Posts: 778
Re: The area of a square garden is A square feet and the  [#permalink]

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20 Dec 2010, 21:03
1
$$a^2=A$$
$$4*a=P$$
$$a^2=8*a+9$$
$$a^2-8a-9=0$$
$$(a-9)(a+1)=0$$
$$a=9$$
$$P=4*a=36$$
Math Expert
Joined: 02 Sep 2009
Posts: 53020
Re: The area of a square garden is A square feet and the  [#permalink]

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14 Dec 2017, 00:38
xmagedo 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/the-area-of- ... 93425.html

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/the-area-of- ... 93425.html
_________________
Re: The area of a square garden is A square feet and the   [#permalink] 14 Dec 2017, 00:38
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