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In the figure above, the area of square ABCD is half the area of recta

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In the figure above, the area of square ABCD is half the area of recta  [#permalink]

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New post 17 Jan 2019, 23:38
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

53% (01:14) correct 48% (01:11) wrong based on 40 sessions

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Re: In the figure above, the area of square ABCD is half the area of recta  [#permalink]

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New post 18 Jan 2019, 04:53
Bunuel wrote:
Image
In the figure above, the area of square ABCD is half the area of rectangle AEFC. What is the ratio of AC to BE?

A 1/4
B 1/3
C 1/2
D 1/1
E 2/1


Attachment:
2019-01-18_1036.png



area of square = 4 ; rectangle = 8
we can say side of square = 2 and rectangle l=4 and breadth = side of square = 2
so the part AC= 2 and BE = AE-AB = 4-2 = 2
so ratio : 2/2 ; 1/1 IMO D
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Re: In the figure above, the area of square ABCD is half the area of recta  [#permalink]

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New post 18 Mar 2019, 06:07
The question basically tells us that the rectangle is exactly twice as big as the square. Thus we can imagine the rectangle consists of two squares the size of our initial square. Hence, the distance of AB is the exact same as BE.

This one can be solved without a single calculation. :)
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Re: In the figure above, the area of square ABCD is half the area of recta  [#permalink]

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New post 19 Mar 2019, 19:11
Bunuel wrote:
Image
In the figure above, the area of square ABCD is half the area of rectangle AEFC. What is the ratio of AC to BE?

A 1/4
B 1/3
C 1/2
D 1/1
E 2/1


Attachment:
2019-01-18_1036.png


We can let the side of square ABCD = the width of rectangle AEFC = 4, and so the length of rectangle AEFC = 8. Since AB = AC = 4, BE = AE - AB = 8 - 4 = 4. Thus the ratio of AC to BE is 4/4 = 1/1.

Answer: D
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Re: In the figure above, the area of square ABCD is half the area of recta   [#permalink] 19 Mar 2019, 19:11
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In the figure above, the area of square ABCD is half the area of recta

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