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

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Manager
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A rectangle s perimeter is P, area is A. Is it a square? 1). [#permalink] New post 31 May 2006, 03:38
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A rectangle’s perimeter is P, area is A. Is it a square?

1). p=4/3A

2). p=4RootA
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 [#permalink] New post 31 May 2006, 04:07
P=2*(A+B)
S=4scrtA*B
then 2(a+b)=4scrta*b, square both sides and get 2a=2b
so B
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 [#permalink] New post 31 May 2006, 04:18
A rectangle’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
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 [#permalink] New post 31 May 2006, 09:17
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.
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 [#permalink] New post 31 May 2006, 10:04
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.
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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 [#permalink] New post 31 May 2006, 12:18
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!
  [#permalink] 31 May 2006, 12:18
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