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

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

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06 Oct 2003, 04:36
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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

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Re: In the figure above, what is the perimeter of rectangle ABPQ [#permalink]

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06 Oct 2003, 10:54
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.

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Re: In the figure above, what is the perimeter of rectangle ABPQ [#permalink]

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06 Oct 2003, 16:12
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]

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06 Aug 2014, 12:01
OA is E

Source: GMAC Test Code 42

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Re: In the figure above, what is the perimeter of rectangle ABPQ [#permalink]

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06 Aug 2014, 15:38
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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.

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Re: In the figure above, what is the perimeter of rectangle ABPQ [#permalink]

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15 Jan 2016, 07:58
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Re: In the figure above, what is the perimeter of rectangle ABPQ [#permalink]

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20 Mar 2016, 06:25
I read in the Manhattan Geometry Guide (13 ed.)
"If two similar triangles have corresponding side lengths in ratio a: b, then their
areas will be in ratio a^2: b^2.
The lengths being compared do not have to be sides— they can represent heights or perimeters. In fact,
the figures do not have to be triangles."

So I guess, the parameters in this case should be in ratio as well.
Can some one explain this to me.

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Re: In the figure above, what is the perimeter of rectangle ABPQ [#permalink]

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20 Mar 2016, 06:41
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rickyfication wrote:
I read in the Manhattan Geometry Guide (13 ed.)
"If two similar triangles have corresponding side lengths in ratio a: b, then their
areas will be in ratio a^2: b^2.
The lengths being compared do not have to be sides— they can represent heights or perimeters. In fact,
the figures do not have to be triangles."

So I guess, the parameters in this case should be in ratio as well.
Can some one explain this to me.

Hi,
you are correct --
If two polygons are similar, their corresponding sides, altitudes, medians, diagonals, angle bisectors and perimeters are all in the same ratio.

but here "You are not given anything about similarity", so you cannot apply the same rule here..
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: In the figure above, what is the perimeter of rectangle ABPQ [#permalink]

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20 Mar 2016, 07:10
chetan2u wrote:
rickyfication wrote:
I read in the Manhattan Geometry Guide (13 ed.)
"If two similar triangles have corresponding side lengths in ratio a: b, then their
areas will be in ratio a^2: b^2.
The lengths being compared do not have to be sides— they can represent heights or perimeters. In fact,
the figures do not have to be triangles."

So I guess, the parameters in this case should be in ratio as well.
Can some one explain this to me.

Hi,
you are correct --
If two polygons are similar, their corresponding sides, altitudes, medians, diagonals, angle bisectors and perimeters are all in the same ratio.

but here "You are not given anything about similarity", so you cannot apply the same rule here..

Thanks, but I am finding it difficult to figure out why ABPQ and ABCD are not similar, since both the figures are rectangle, they have one common side therefore PQ has to be || with CD. is there anything wrong with my concept??

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Re: In the figure above, what is the perimeter of rectangle ABPQ [#permalink]

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20 Mar 2016, 07:21
rickyfication wrote:
chetan2u wrote:
rickyfication wrote:
I read in the Manhattan Geometry Guide (13 ed.)
"If two similar triangles have corresponding side lengths in ratio a: b, then their
areas will be in ratio a^2: b^2.
The lengths being compared do not have to be sides— they can represent heights or perimeters. In fact,
the figures do not have to be triangles."

So I guess, the parameters in this case should be in ratio as well.
Can some one explain this to me.

Hi,
you are correct --
If two polygons are similar, their corresponding sides, altitudes, medians, diagonals, angle bisectors and perimeters are all in the same ratio.

but here "You are not given anything about similarity", so you cannot apply the same rule here..

Thanks, but I am finding it difficult to figure out why ABPQ and ABCD are not similar, since both the figures are rectangle, they have one common side therefore PQ has to be || with CD. is there anything wrong with my concept??

Hi,
since you are also saying one side is equal and the other two side are lesser than their corresponding sides ..
this basically means the sides are not in the same ratio..
whereas ONE set of sides have ratio as 1, the OTHER set is not 1, but something else..
for two triangles - ONE has L= 2 and B= 1, th eOTHER has L=6 and B=3.. these triangles are similar as ratios of sides 2/6 is same as 1/3
BUT if ONE has L= 2 and B= 1, th eOTHER has L=6 and B=1.. these triangles are NOT similar as ratios of sides 2/6 is NOT same as 1/1

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Re: In the figure above, what is the perimeter of rectangle ABPQ [#permalink]

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20 Mar 2016, 07:42
Got you point Chetan. Thanks for the clarification.

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Re: In the figure above, what is the perimeter of rectangle ABPQ [#permalink]

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14 Apr 2017, 00:23
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In the figure above, what is the perimeter of rectangle ABPQ [#permalink]

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19 Jun 2017, 03:22
Lets dive into statement analysis straight away:

Stmt 1: Since AB is common width between 2 figures, clearly the length of larger rectangle ABCD should be 3 times the length of smaller rectangle ABPQ. But using this alone we dont have concrete values to work with. Hence (1) is insufficient.
Stmt 2: Perimeter of ABCD = 54.
= > 2(l+b) =54
=> l+b = 27. This does not give any clue about the smaller rectangle. Hence (2) is insufficient.

Using (1) & (2)
=> 3l' + b = 27. (where l' is length of ABPQ)
We can't solve this further to get 2(l'+b). Hence E.
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Re: In the figure above, what is the perimeter of rectangle ABPQ   [#permalink] 19 Jun 2017, 03:22
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