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# Equilateral triangle BDF is inscribed in equilateral triangle ACE, as

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Equilateral triangle BDF is inscribed in equilateral triangle ACE, as  [#permalink]

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13 Oct 2018, 09:34
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Difficulty:

55% (hard)

Question Stats:

45% (02:18) correct 55% (01:32) wrong based on 19 sessions

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Equilateral triangle BDF is inscribed in equilateral triangle ACE, as shown in the figure above. The shaded region is what fraction of the area of triangle ACE ?
(1) ∠DFE = 90°
(2) The length of AF is $$10\sqrt{3}$$

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Re: Equilateral triangle BDF is inscribed in equilateral triangle ACE, as  [#permalink]

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13 Oct 2018, 09:41
Equilateral triangle BDF is inscribed in equilateral triangle ACE, as shown in the figure above. The shaded region is what fraction of the area of triangle ACE ?
(1) ∠DFE = 90°
(2) The length of AF is 103‾√

C
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Re: Equilateral triangle BDF is inscribed in equilateral triangle ACE, as  [#permalink]

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13 Oct 2018, 09:48
THe answer to this question could be (A) . Please find my solution attached.

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Re: Equilateral triangle BDF is inscribed in equilateral triangle ACE, as  [#permalink]

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13 Oct 2018, 09:50
Statement 1:
We know Angle DEF = 60, Angle DFE=90 so Angle EDF = 30. This basically gives us the ratio of sides DF:FE:ED = Sqrt3:1:2. From this we can derive the ratio of the sides of the Bigger triangle. And we can easily get the area of the shaded region.

Eliminate B, C, E.

Statement 2:
Tells only about AF and nothing about any other sides or angles. So there might be many triangles with this length of AF.
Insufficient.

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Re: Equilateral triangle BDF is inscribed in equilateral triangle ACE, as  [#permalink]

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13 Oct 2018, 10:11
(1) ∠DFE = 90° .......NS........ will not get the area
(2) The length of AF is 10root 3 .......NS...... will not get the area

1+2) can calculate all the areas of the trangles.....thus Suff Ans C
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Re: Equilateral triangle BDF is inscribed in equilateral triangle ACE, as   [#permalink] 13 Oct 2018, 10:11
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