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In trapezoid ABCD we have AB parallel to DC, E as the midpoint of BC,

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Math Expert
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Joined: 02 Sep 2009
Posts: 54493
In trapezoid ABCD we have AB parallel to DC, E as the midpoint of BC,  [#permalink]

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New post 25 Mar 2019, 00:08
1
1
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

23% (02:03) correct 77% (02:48) wrong based on 13 sessions

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Intern
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B
Joined: 07 Sep 2018
Posts: 1
Re: In trapezoid ABCD we have AB parallel to DC, E as the midpoint of BC,  [#permalink]

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New post 25 Mar 2019, 04:01
Because F and E are midpoints of AD and BC respectively, we can assume both trapezoids ABEF and FECD have identical height h and assume h = 1 for simplicity.
Then the area of the larger trapezoid ABEF = 0.5(AB+EF)*h = 0.5AB + 0.5EF.
Then the area of the smaller trapezoid FECD = 0.5(EF+CD)*h = 0.5EF + 0.5CD.
Since F and E are midpoints on DA and BC, EF = 0.5(AB + CD) = 0.5AB + 0.5CD.
Area(ABEF) = 0.5AB + 0.5(0.5AB + 0.5CD) = 0.75AB + 0.25CD
Area(FECD) = 0.5(0.5AB + 0.5CD) + 0.5CD = 0.25AB + 0.75CD
Area(ABEF) / Area(FECD) = 2 -> Area(ABEF) = 2 * Area(FECD) -> 0.75AB + 0.25CD = 2(0.25AB + 0.75CD) -> 0.75AB + 0.25CD = 0.5AB + 1.5CD -> 0.25AB = 1.25CD -> AB/CD = 5

Therefore, IMO the answer is (C)
GMAT Club Bot
Re: In trapezoid ABCD we have AB parallel to DC, E as the midpoint of BC,   [#permalink] 25 Mar 2019, 04:01
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In trapezoid ABCD we have AB parallel to DC, E as the midpoint of BC,

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