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A trapezoid ABCD has sides BC and AD parallel to each other, while AB

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A trapezoid ABCD has sides BC and AD parallel to each other, while AB  [#permalink]

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New post 17 Jul 2018, 23:43
1
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A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

13% (02:21) correct 87% (02:40) wrong based on 15 sessions

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A trapezoid ABCD has sides BC and AD parallel to each other, while AB and CD are not parallel. A point E lies on side AD such that CE is perpendicular to AD. Area of triangle CED is what fraction of area of trapezoid ABCD?

(1) ABCD is an isosceles trapezoid with AB = 6 units.

(2) Angle DCE = 60 degrees.
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Re: A trapezoid ABCD has sides BC and AD parallel to each other, while AB  [#permalink]

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New post 18 Jul 2018, 00:18
amanvermagmat wrote:
A trapezoid ABCD has sides BC and AD parallel to each other, while AB and CD are not parallel. A point E lies on side AD such that CE is perpendicular to AD. Area of triangle CED is what fraction of area of trapezoid ABCD?

(1) ABCD is an isosceles trapezoid with AB = 6 units.

(2) Angle DCE = 60 degrees.


Since the trapezoid and the triangle share the same height, CE, to know the ratio of their areas we need to know the ratio of their bases.
That is, we need to know ED : (BC + CD)
We'll look for statements that give us this information, a Logical approach.

(1) This doesn't help us calculate the lengths of the bases.
Insufficient.

(2) This give us one of the angles in the triangle. But what is the ratio between the lengths of the bases?
Insufficient.

Combined:
We now know that CED is a 30-60-90 triangle and know the length of one of its sides so we can calculate the other two.
But - we still have no information on the length of the base BC and cannot calculate what we need.
Insufficient.

(E) is our answer.
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Re: A trapezoid ABCD has sides BC and AD parallel to each other, while AB &nbs [#permalink] 18 Jul 2018, 00:18
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