Equilateral triangle BDF is inscribed in equilateral triangle ACE, as

Question

Q.jpg 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} Weekly Quant Quiz #4 Ques 8

Archit3110 · Answer

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

Gladiator59 · Answer

THe answer to this question could be (A) . Please find my solution attached.

Regards,
GLadi

sushforgmat · Answer

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.

Answer = A

u1983 · Answer

(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

mohagar · Answer

howw long did u take to solve this question

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Equilateral triangle BDF is inscribed in equilateral triangle ACE, as

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