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Math Expert V
Joined: 02 Sep 2009
Posts: 55661
The midpoints of the sides of square ABCD above are connected to form  [#permalink]

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Difficulty:   15% (low)

Question Stats: 85% (01:28) correct 15% (01:19) wrong based on 32 sessions

HideShow timer Statistics The midpoints of the sides of square ABCD above are connected to form square EFGH. What is the ratio of the area of square EFGH to the area of square ABCD?

A. 1/4

B. 1/3

C. 1/2

D. $$\frac{1}{\sqrt{2}}$$

E. 2/1

Attachment: 2019-01-11_1254.png [ 15.87 KiB | Viewed 401 times ]

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Manager  G
Joined: 28 Aug 2018
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Re: The midpoints of the sides of square ABCD above are connected to form  [#permalink]

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IMO C

AB side is x...area s x2

EF side is x/square root of 2..... area is x2/2

EF: AB (area)=1/2
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Re: The midpoints of the sides of square ABCD above are connected to form  [#permalink]

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Bunuel wrote: The midpoints of the sides of square ABCD above are connected to form square EFGH. What is the ratio of the area of square EFGH to the area of square ABCD?

A. 1/4

B. 1/3

C. 1/2

D. $$\frac{1}{\sqrt{2}}$$

E. 2/1

Attachment:
2019-01-11_1254.png

let square abcd = 4 and efgh will be 2 sqrt2

so 8/4*4 = 1/2 IMO C
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Re: The midpoints of the sides of square ABCD above are connected to form  [#permalink]

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In square EFGH, side EF=diagonal/(2)^1/2= EG/sqrt 2
Area of square EFGH= EF^2= (EG^2)/2
Area of sqaure ABCD= AB^2= EG^2

So, ration of area EFGH/area ABCD={( EG^2)/2}/EG^2= 1/2 Re: The midpoints of the sides of square ABCD above are connected to form   [#permalink] 11 Jan 2019, 12:00
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