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# What is the area of the region in which squares ABCD and EFGH overlap?

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What is the area of the region in which squares ABCD and EFGH overlap?  [#permalink]

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16 Jun 2014, 21:51
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55% (hard)

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55% (01:43) correct 45% (01:40) wrong based on 183 sessions

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What is the area of the region in which squares ABCD and EFGH overlap?

(1) EF bisects BC.

(2) The distance from point C to point E is $$2\sqrt{2}$$ and the distance from point C to point F is $$2\sqrt{2}$$.

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Re: What is the area of the region in which squares ABCD and EFGH overlap?  [#permalink]

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16 Jun 2014, 22:42
Gnpth wrote:
What is the area of the region in which squares ABCD and EFGH overlap?

STATEMENT 1:

EF bisects BC.

STATEMENT 2:

The distance from point C to point E is $$2\sqrt{2}$$ and the distance from point C to point F is $$2\sqrt{2}$$.

Quote:
Image Attached

St 1 says: EF bisects BC. Let the Point of intersection be X. Thus we have BX+XC=BC. If CX=a then EY= b where Y is the pt of intersection between EH and CD.
Now we can say EY=XC=a but we don't know if EY is equal to CX or not.Thus we cannot find length of Square EFGH

St 2 says : CE is $$2\sqrt{2}$$ and the distance from point C to point F is [m]2\sqrt{2}

Consider triangle ECX where X is the point of intersection of BC and EF...We will get a triangle with angles 45:45:90...and thus we can find CX=2 and EX=2...Implying EXCY is a square. We can get the answer.

So B
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Re: What is the area of the region in which squares ABCD and EFGH overlap?  [#permalink]

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30 Sep 2014, 03:44
How did you deduce that triangle ECX is a 45:45:90 triangle?

WoundedTiger wrote:
Gnpth wrote:
What is the area of the region in which squares ABCD and EFGH overlap?

STATEMENT 1:

EF bisects BC.

STATEMENT 2:

The distance from point C to point E is $$2\sqrt{2}$$ and the distance from point C to point F is $$2\sqrt{2}$$.

Quote:
Image Attached

St 1 says: EF bisects BC. Let the Point of intersection be X. Thus we have BX+XC=BC. If CX=a then EY= b where Y is the pt of intersection between EH and CD.
Now we can say EY=XC=a but we don't know if EY is equal to CX or not.Thus we cannot find length of Square EFGH

St 2 says : CE is $$2\sqrt{2}$$ and the distance from point C to point F is [m]2\sqrt{2}

Consider triangle ECX where X is the point of intersection of BC and EF...We will get a triangle with angles 45:45:90...and thus we can find CX=2 and EX=2...Implying EXCY is a square. We can get the answer.

So B
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Re: What is the area of the region in which squares ABCD and EFGH overlap?  [#permalink]

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08 Oct 2014, 03:06
Well,i doubt whether v can prove if 45-45-90 is possible here..

A is clearly insufficient.

stmnt B=
let midpt of BC be - x

Hence, BX=BC=2 ----- GIVEN
Now,as triangle EXC is right angled,and as we know the 2 given sides of that triangle we can find Side EX...

Now,let Y be point on side DC...if we observe EY has length similar to that of XC..We can clearly say that EY=XC=2..

Therefore, as we know that triangle EYC is right angled and as we know 2 sides,by using pythagoras,we can find the remaining side..

hence we have found the values of all sides,we can find its area..
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Re: What is the area of the region in which squares ABCD and EFGH overlap?  [#permalink]

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04 Aug 2016, 17:27
Gnpth wrote:
Attachment:
Problem.JPG
What is the area of the region in which squares ABCD and EFGH overlap?

(1) EF bisects BC.

(2) The distance from point C to point E is $$2\sqrt{2}$$ and the distance from point C to point F is $$2\sqrt{2}$$.

Stat 1: EF bisects BC means EF is divided into two parts exactly. Then we can understand that the overlapped region is quarter of the two square. But we don't have enough information whether BC is also exactly half of EF then it would have been the quarter region of each square..Insufficient.

Stat 2: (From figure ) EF is diagonal of smaller square and value is $$2\sqrt{2}$$. Since $$2\sqrt{2}$$^2 + $$2\sqrt{2}$$^2 = 4 ( pythogarous theorem) and quarter square diagonal is half of full diagonal.

=>$$a\sqrt{2}$$ = $$2\sqrt{2}$$

a = 2. From this we can know the area of smaller square..Sufficient..

Option B is correct.
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Re: What is the area of the region in which squares ABCD and EFGH overlap?  [#permalink]

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24 Jan 2018, 10:58
we must know the term "bisect" which means the line is divided into 2 equal parts. Hence, from st1, we cannot conclude much.
Re: What is the area of the region in which squares ABCD and EFGH overlap?   [#permalink] 24 Jan 2018, 10:58
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