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# A rectangle s perimeter is P, area is A. Is it a square? 1).

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Manager
Joined: 04 Dec 2005
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A rectangle s perimeter is P, area is A. Is it a square? 1). [#permalink]  31 May 2006, 03:38
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A rectangleâ€™s perimeter is P, area is A. Is it a square?

1). p=4/3A

2). p=4RootA
Director
Joined: 13 Nov 2003
Posts: 790
Location: BULGARIA
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P=2*(A+B)
S=4scrtA*B
then 2(a+b)=4scrta*b, square both sides and get 2a=2b
so B
Manager
Joined: 29 Sep 2005
Posts: 125
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Kudos [?]: 2 [0], given: 0

A rectangleâ€™s perimeter is P, area is A. Is it a square?

1). p=4/3A

2). p=4RootA

********************************************

I would go with B

From the question stem:

2(l+w) = P --(1)
lw = A

From Statement 1:

P = 4/3 A -- substitue this in (1)

2(l+w) = 4/3 lw
6(l+w) = 4 lw
3(l+w) = 2 lw ----Insuff.

From Statement 2:

P = 4(sqrt A)

Substitue this in (1)

l+w = 2(sqrt lw)
square both sides and get a quadratic

l^2 + -2lw +w^2 = 0

(l-w)^2 = 0

[b]l-w has to be positive --------> Can someone pls. confirm if this logic is correct?[/b]

so L = W and it is a square
Manager
Joined: 10 May 2006
Posts: 186
Location: USA
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Kudos [?]: 3 [0], given: 0

From Statement 2:

P = 4(sqrt A)

Substitue this in (1)

l+w = 2(sqrt lw)
square both sides and get a quadratic

l^2 + -2lw +w^2 = 0

(l-w)^2 = 0

l-w has to be positive --------> Can someone pls. confirm if this logic is correct?

so L = W and it is a square[/quote]

Regarding your question on, l-w^=0 I would explain it as...because l-w = 0, l must equal w.
CEO
Joined: 20 Nov 2005
Posts: 2910
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 19

Kudos [?]: 132 [0], given: 0

B

Lets say the rectangle has sides x and y then
A = xy
P = 2(x+y)

St1: 2(x+y) = 4/3 (xy). No conclusion. INSUFF

St2: 2(x+y) = 4 SQRT(xy)

This leads us to 4 (x+y)^2 = 16xy i.e 4 (x-y)^2 = 0 i.e x=y. Its a square. SUFF.
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Manager
Joined: 29 Sep 2005
Posts: 125
Followers: 1

Kudos [?]: 2 [0], given: 0

tl372 wrote:
From Statement 2:

P = 4(sqrt A)

Substitue this in (1)

l+w = 2(sqrt lw)
square both sides and get a quadratic

l^2 + -2lw +w^2 = 0

(l-w)^2 = 0

l-w has to be positive --------> Can someone pls. confirm if this logic is correct?

so L = W and it is a square

Regarding your question on, l-w^=0 I would explain it as...because l-w = 0, l must equal w.[/quote]

Thanks tl372!
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