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Manager  Joined: 27 Jul 2003
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In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 66% (02:18) correct 34% (01:35) wrong based on 567 sessions

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Attachment: Untitled.png [ 1.18 KiB | Viewed 8787 times ]
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.
Manager  Joined: 26 Aug 2003
Posts: 222
Location: United States
Re: In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

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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  Joined: 15 Aug 2003
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Re: In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

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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?

My answer E.

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

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1
1
Attachment: Screen shot 2014-08-07 at 12.21.12 AM.png [ 9.48 KiB | Viewed 8748 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.

Not sufficient, answer E
Intern  B
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Re: In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

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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.
Math Expert V
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Posts: 7686
Re: In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

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1
1
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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Re: In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

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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??
Math Expert V
Joined: 02 Aug 2009
Posts: 7686
Re: In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

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1
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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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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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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In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

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Top Contributor
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araspai wrote:
Attachment:
Untitled.png
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.

Target question: What is the perimeter of rectangle ABPQ?

Statement 1: The area of rectangular region ABCD is 3 times the area of rectangular region ABPQ.
Since we aren't given any information regarding ACTUAL lengths, we cannot determine the perimeter of rectangle ABPQ
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The perimeter of rectangle ABCD is 54
There are many possible cases in which ABCD's perimeter is 54, yet the perimeter of rectangle ABPQ is not fixed (see diagrams below)
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several scenarios that satisfy BOTH statements. Here are two:

Case a: The measurements are as follows: Notice that the area of ABCD (72 square units) is 3 times the area of rectangular region ABPQ (24 square units)
Also notice that ABCD has perimeter 54
In this case, the perimeter of rectangle ABPQ = 1 + 24 + 1 + 24 = 50

Case b: The measurements are as follows: Notice that the area of ABCD (126 square units) is 3 times the area of rectangular region ABPQ (42 square units)
Also notice that ABCD has perimeter 54
In this case, the perimeter of rectangle ABPQ = 2 + 21 + 2 + 21 = 46

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
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Originally posted by GMATPrepNow on 26 Feb 2018, 16:15.
Last edited by GMATPrepNow on 16 Apr 2018, 12:15, edited 1 time in total.
Intern  B
Joined: 20 Dec 2017
Posts: 36
Location: Singapore
Re: In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

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I notice that this is quite a common trick question on areas/perimeters that and can be solved very quickly.

Basically for rectangles, the perimeter and area may not be proportionate to each other (do correct me if I am wrong)

For example a 100 sqft rectangle could be:
1) 100 + 100 + 1 +1 = 202 ft perimeter
2) 20 + 20 + 5 + 5 = 50 ft perimeter

Back to the question,
(1) The area ratio is given, but nothing about the perimeter. Also, the question is asking for a specific value which the statement does not provide any clue - Insufficient
(2) Although the perimeter of ABCD is given, it does not show how ABCD and ABPQ are related to each other - Insufficient
(1) & (2) Since area and perimeter are not proportionate, not possible to derive answer without also knowing any side lengths - Insufficient

Hence answer is (E)

If the question was on a square, then it would have been (C) since we could derive the length of its sides from statement (2)
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Re: In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

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_________________ Re: In the figure above, what is the perimeter of rectangle ABPQ   [#permalink] 08 Mar 2019, 08:25
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