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

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Manager
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The area of a square garden is A square feet and the [#permalink]

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New post 26 Jul 2010, 00:56
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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
[Reveal] Spoiler: OA
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Manager
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Re: The area of a square garden is A square feet and the [#permalink]

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New post 26 Jul 2010, 01:39
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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
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Re: The area of a square garden is A square feet and the [#permalink]

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New post 26 Jul 2010, 01:49
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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 \(x=9\) --> \(perimeter=p=4x=36\).

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

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New post 26 Jul 2010, 01:54
Pleas can you explain how x=9 ? I didnt get this point
thanks
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Re: The area of a square garden is A square feet and the [#permalink]

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New post 26 Jul 2010, 02:30
Senior Manager
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Re: The area of a square garden is A square feet and the [#permalink]

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New post 26 Jul 2010, 18:24
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
Manager
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Re: The area of a square garden is A square feet and the [#permalink]

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New post 27 Jul 2010, 03:42
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
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Re: The area of a square garden is A square feet and the [#permalink]

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New post 20 Dec 2010, 22:03
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\(a^2=A\)
\(4*a=P\)
\(a^2=8*a+9\)
\(a^2-8a-9=0\)
\((a-9)(a+1)=0\)
\(a=9\)
\(P=4*a=36\)
Thus answer is B
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Posts: 44634
Re: The area of a square garden is A square feet and the [#permalink]

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New post 14 Dec 2017, 01:38
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
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Re: The area of a square garden is A square feet and the   [#permalink] 14 Dec 2017, 01:38
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