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# In the figure above, what is the perimeter of rectangle ABPQ

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Manager
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In the figure above, what is the perimeter of rectangle ABPQ [#permalink]  06 Oct 2003, 03:36
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In the figure above, what is the perimeter of rectangle ABPQ?

(1) The area of rectangular region ABCD is 3 times the area of rectangular region ABPQ.
(2) The perimeter of rectangle ABCD is 54.
[Reveal] Spoiler: OA
Manager
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Re: In the figure above, what is the perimeter of rectangle ABPQ [#permalink]  06 Oct 2003, 09:54
C?

My first would have been E, but then I saw AB was common in both rectangles, so I decided to answer C. But I decided to do a little calculation to verify. That took me like three-four minutes. Now seems like C is a good choice.
CEO
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Re: In the figure above, what is the perimeter of rectangle ABPQ [#permalink]  06 Oct 2003, 15:12
araspai wrote:
ABPQ is a smaller rectangle within a bigger rectangle ABCD, what is the peimeter of the rectangle ABPQ?
a. The area of rectangular region ABCD is 3 times the area of the rectangular region ABPQ.
b. The perimeter of bigger rectangle ABCD is 54.

A...clearly insufficient ..we only know A [ ABPQ] = 1/3 * A[ABCD]
3 * L * W1 = L * W
W = 3 W1
B... clearly insufficient
L + W = 27 ....

combine....
A[ ABPQ] = LW/3

L + W =27 W = 27 - L . W1 = 27 - L / 3

Perimeter of ABPQ = 2 L + 2 (27 - L /3)

I dont see how Wonder got C...what did i miss?

Thanks
praetorian
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Re: In the figure above, what is the perimeter of rectangle ABPQ [#permalink]  06 Aug 2014, 11:01
OA is E

Source: GMAC Test Code 42
Manager
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Re: In the figure above, what is the perimeter of rectangle ABPQ [#permalink]  06 Aug 2014, 14:38
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Screen shot 2014-08-07 at 12.21.12 AM.png [ 9.48 KiB | Viewed 991 times ]

Let the sides of ABCD be x and y.
Let the sides of ABPQ be x1 and y.

We want to find $$2x1+2y=?$$

1) tells us : $$2x+2y=54$$ not sufficient
2) tells us $$xy=3*x1*y$$, $$x=3*x1$$ not sufficient

1+2) tells us $$6x1+2y=54$$, so $$3x1+y=27$$

x1 could be equal to 1 and y to 24
or x1 could be equal to 2 and y 21 etc.

Re: In the figure above, what is the perimeter of rectangle ABPQ   [#permalink] 06 Aug 2014, 14:38
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