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# In the figure above, the area of the square EFGH is what percent of

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Joined: 02 Sep 2009
Posts: 49985
In the figure above, the area of the square EFGH is what percent of  [#permalink]

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09 Nov 2017, 23:29
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Difficulty:

35% (medium)

Question Stats:

87% (01:33) correct 13% (01:30) wrong based on 28 sessions

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In the figure above, the area of the square EFGH is what percent of the area of the square region ABCD?

(A) 16 2/3%
(B) 12 1/2%
(C) 12%
(D) 8 1/2%
(E) 8%

Attachment:

2017-11-07_0942_002.png [ 6.12 KiB | Viewed 705 times ]

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Re: In the figure above, the area of the square EFGH is what percent of  [#permalink]

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10 Nov 2017, 00:26
Taken that ABCD is square, relationship of inner sides of triangle AGD is 2^1/2 / 1 / 1

Area ABCD = (2^1/2)^2 = 2
Area AGD = 1/2 * 1 * 1 = 1/2
Area FGHE = 1/2*1/2 = 1/4 (taken that side of squre FGHE is equal to half of side of triangle AGD)

Area FGHE / Area ABCD = 1/4 / 2 = 1/8 or 12,5%

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In the figure above, the area of the square EFGH is what percent of  [#permalink]

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11 Nov 2017, 04:19
Bunuel wrote:

In the figure above, the area of the square EFGH is what percent of the area of the square region ABCD?

(A) 16 2/3%
(B) 12 1/2%
(C) 12%
(D) 8 1/2%
(E) 8%

Attachment:
2017-11-07_0942_002.png

Let Side = a, Daignol = root(2)a
Each side of EFGH = a/2root(2)
Area of EFGH = a/8.
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Re: In the figure above, the area of the square EFGH is what percent of  [#permalink]

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11 Nov 2017, 05:43
rahul16singh28 wrote:
Bunuel wrote:

In the figure above, the area of the square EFGH is what percent of the area of the square region ABCD?

(A) 16 2/3%
(B) 12 1/2%
(C) 12%
(D) 8 1/2%
(E) 8%

Attachment:
2017-11-07_0942_002.png

Let Side = a, Daignol = root(2)a
Each side of EFGH = a/2root(2)
Area of EFGH = a/8.

Let total Area of the square is 8
area of Triangle AGD is one fourth of total area.
so area is of triangle is 2.
area of EFGH is 1.
now calculate percentage area by dividing 1by 8 multiple by 100.
which is 25/2
Re: In the figure above, the area of the square EFGH is what percent of &nbs [#permalink] 11 Nov 2017, 05:43
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