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In square ABCD above, if DE = 2EB, then the area of the shaded region

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In square ABCD above, if DE = 2EB, then the area of the shaded region  [#permalink]

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New post 14 Sep 2018, 00:52
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In square ABCD above, if DE = 2EB, then the area of the shaded region is what fraction of the area of the square region ABCD?


A. 1/9

B. 2/9

C. 1/6

D. 1/3

E. 2/3


Attachment:
image029.gif
image029.gif [ 1.85 KiB | Viewed 404 times ]

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In square ABCD above, if DE = 2EB, then the area of the shaded region  [#permalink]

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New post Updated on: 14 Sep 2018, 01:33
Bunuel wrote:
Image
In square ABCD above, if DE = 2EB, then the area of the shaded region is what fraction of the area of the square region ABCD?


A. 1/9

B. 2/9

C. 1/6

D. 1/3

E. 2/3


Attachment:
image029.gif


Diagonal Divides the square into two equal halfs

DE = 2EB means that bases of similar triangles DBC and DEF are in the ratio 2/3 (Ratio of corresponding sides in similar triangles are equal)
hence ratio of areas of DEF to DBC = (2/3)^2 = 4/9
i.e. DEF = 4/9 of triangle DBC

i.e. Shaded region = (1/2)*(4/9)* Area of square
i.e. Shaded region = (2/9)* Area of square

Answer: Option B
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Originally posted by GMATinsight on 14 Sep 2018, 01:06.
Last edited by GMATinsight on 14 Sep 2018, 01:33, edited 1 time in total.
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Re: In square ABCD above, if DE = 2EB, then the area of the shaded region  [#permalink]

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New post 14 Sep 2018, 01:29
Bunuel wrote:
Image
In square ABCD above, if DE = 2EB, then the area of the shaded region is what fraction of the area of the square region ABCD?


A. 1/9

B. 2/9

C. 1/6

D. 1/3

E. 2/3


Attachment:
image029.gif


When two Triangles are Similar. their Area is in the Ratio of the squares of their side.

Hence, \(\frac{Area of Tr. DEF}{Area of Tr. BCD} = \frac{4}{9}\) or

\(\frac{Area of Tr. DEF}{2*Area of Tr. BCD} = \frac{2}{9}\)

Hence, B.
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Re: In square ABCD above, if DE = 2EB, then the area of the shaded region  [#permalink]

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New post 14 Sep 2018, 01:44
Hi GMAT Insight,

While considering similar triangles, if the sides are in the ratio 2/3 then shoudn't the area be in the ratio (2/3)^2.

I am getting the below based on the above assumptions.

Shaded region = (1/2)x (2/3)^2 Area of ABCD
Shaded region = (1/2)x (4/9) Area of square
Shaded region = (2/9) Area of square
Which is answer B.

Pls clarify
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Re: In square ABCD above, if DE = 2EB, then the area of the shaded region  [#permalink]

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New post 14 Sep 2018, 11:24
1
Bunuel wrote:
Image
In square ABCD above, if DE = 2EB, then the area of the shaded region is what fraction of the area of the square region ABCD?


A. 1/9

B. 2/9

C. 1/6

D. 1/3

E. 2/3


Attachment:
image029.gif


If the diagonal is divided into 2:1 that means total is 3.
the lines drawn are 8, so we can assume that if the entire square has lines then we will have 12 lines.

so we can say that the bigger square is 12 units in lenght. so it is 12*12=144 units area.

the smaller square will be 8*8=64 units.but shaded is half the total area of the smaller square. so 64/2=32 units.

now question ask abt shaded to total, we get 32/144=2/9.

Option B.2/9
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Re: In square ABCD above, if DE = 2EB, then the area of the shaded region &nbs [#permalink] 14 Sep 2018, 11:24
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