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# If angle ABC is 30 degrees, what is the area of triangle BCE?

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Math Expert
Joined: 02 Sep 2009
Posts: 60465
If angle ABC is 30 degrees, what is the area of triangle BCE?  [#permalink]

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05 Nov 2019, 06:00
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Difficulty:

75% (hard)

Question Stats:

52% (02:37) correct 48% (03:23) wrong based on 48 sessions

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If angle ABC is 30 degrees, what is the area of triangle BCE?

(1) Angle CDF is 120 degrees, lines L and M are parallel, and AC = 6, BC = 12, and EC = 2AC
(2) Angle DCG is 60 degrees, angle CDG is 30 degrees, angle FDG = 90, and GC = 6, CD = 12 and EC = 12

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If angle ABC is 30 degrees, what is the area of triangle BCE?  [#permalink]

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05 Nov 2019, 08:49
If angle ABC is 30 degrees, what is the area of triangle BCE?

STATEMENT (1) Angle CDF is 120 degrees, lines L and M are parallel, and AC = 6, BC = 12, and EC = 2AC

in triangle BCE
BC = 12 and EC = 12 (this proves that BCE is isosceles triangle)
now AB bisects side EC in two equal parts
AB is the median = altitude = angle bisector (since BCE is an isosceles triangle)
we can find the altitude AB
now we can find the area of triangle BCE
SUFFICIENT

STATEMENT (2) Angle DCG is 60 degrees, angle CDG is 30 degrees, angle FDG = 90, and GC = 6, CD = 12 and EC = 12

in triangle BCE
EC = 12 (base) we need to know the height of the triangle

angle DGC = 90
height of triangle BCE = DGC that is = 6
now we know the base of triangle BCE = 12
height of BCE = 6
We can find the area
SUFFICIENT

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Re: If angle ABC is 30 degrees, what is the area of triangle BCE?  [#permalink]

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05 Nov 2019, 22:24

As

Option one we can easily find the area of triangle being equilateral as we know the angle.

So we AD/BCE one is sufficient

Now in second point the two lines are parallel meaning which both trainable are same

So D

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Re: If angle ABC is 30 degrees, what is the area of triangle BCE?  [#permalink]

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30 Dec 2019, 10:14
shridhar786 wrote:
height of triangle BCE = DGC that is = 6

I am being picky here, but the height is actually $$6\sqrt{2}$$

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Re: If angle ABC is 30 degrees, what is the area of triangle BCE?  [#permalink]

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17 Jan 2020, 01:16
Very good question...worth trying !!!
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Re: If angle ABC is 30 degrees, what is the area of triangle BCE?   [#permalink] 17 Jan 2020, 01:16
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