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

\(A=l * l =l^2\)

\(P= 4l\)

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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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

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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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

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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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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I used this method,but end up with a complex quadratic equation - P^2-32P-144=0 Any quick ways to solve for p from that quadratic equation?

Note that the equation has negative coefficient of P and a negative constant term.
So sum of roots and product of roots both are negative. Hence one root is negative and the other positive. So at least one root will be greater than 32. Since the product of both is 144, the other root will be very small such as 2, 3 or 4. You see that 36*4 = 144 so you get the split as

P^2 - 36P + 4P - 144 = 0
(P - 36)(P + 4) = 0
P = 36
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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.

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