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Math Expert V
Joined: 02 Sep 2009
Posts: 58421
In the figure above, the area of square ABCD is half the area of recta  [#permalink]

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Difficulty:   55% (hard)

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

HideShow timer Statistics 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 [ 4.42 KiB | Viewed 545 times ]

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Posts: 5026
Location: India
Concentration: Sustainability, Marketing
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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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Bunuel wrote: 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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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.

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Target Test Prep Representative D
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Posts: 8117
Location: United States (CA)
Re: In the figure above, the area of square ABCD is half the area of recta  [#permalink]

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Bunuel wrote: 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.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. 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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