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Re: The area of a square garden is A square feet and the perimet [#permalink]
24 Sep 2012, 10:30

2

This post received KUDOS

Expert's post

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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 \(x=9\) --> \(perimeter=p=4x=36\).

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

Re: The area of a square garden is A square feet and the perimet [#permalink]
13 Nov 2013, 13:42

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Re: The area of a square garden is A square feet and the perimet [#permalink]
19 Nov 2014, 06:26

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Re: The area of a square garden is A square feet and the perimet [#permalink]
11 Jan 2015, 04:21

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!

Re: The area of a square garden is A square feet and the perimet [#permalink]
26 Jan 2015, 16:45

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" . _________________

Re: The area of a square garden is A square feet and the perimet [#permalink]
26 Jan 2015, 21:30

Expert's post

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 _________________

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