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# The midpoints of the sides of square ABCD above are connected to form

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

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11 Jan 2019, 01:56
00:00

Difficulty:

15% (low)

Question Stats:

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

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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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Re: The midpoints of the sides of square ABCD above are connected to form  [#permalink]

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11 Jan 2019, 02:03
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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11 Jan 2019, 04:46
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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11 Jan 2019, 12:00
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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