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# In the figure, ABCD is a rectangle. The area of quadrilateral EBFD is

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Joined: 02 Sep 2009
Posts: 59725
In the figure, ABCD is a rectangle. The area of quadrilateral EBFD is  [#permalink]

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Updated on: 08 Oct 2019, 23:26
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Difficulty:

55% (hard)

Question Stats:

58% (02:25) correct 42% (02:11) wrong based on 19 sessions

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In the figure, ABCD is a rectangle. The area of quadrilateral EBFD is one-half the area of the rectangle ABCD. Which one of the following is the value of AD ?

(A) 5

(B) 6

(C) 7

(D) 12

(E) 15

Attachment:

#GREpracticequestion In the figure, ABCD is a rectangle..jpg [ 22.21 KiB | Viewed 632 times ]

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Originally posted by Bunuel on 17 Mar 2019, 23:51.
Last edited by Bunuel on 08 Oct 2019, 23:26, edited 2 times in total.
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Joined: 12 Sep 2015
Posts: 4154
Re: In the figure, ABCD is a rectangle. The area of quadrilateral EBFD is  [#permalink]

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18 Mar 2019, 06:34
Top Contributor
Bunuel wrote:

In the figure, ABCD is a rectangle. The area of quadrilateral EBFD is one-half the area of the rectangle ABCD. Which one of the following is the value of AD ?

(A) 5

(B) 6

(C) 7

(D) 12

(E) 15

Attachment:
#GREpracticequestion In the figure, ABCD is a rectangle..jpg

APPROACH #1:
IMPORTANT: the diagrams in GMAT problem solving questions are DRAWN TO SCALE unless stated otherwise.

So, we can use this fact to solve the question by simply "eyeballing" the diagram.

Since ED = 3, we know that AE is a little by longer than 3
I'd say that AE has length 4 or 5
So, AD has a total length of 7 or 8

Only answer choice C is close to our estimate.

Cheers,
Brent
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Joined: 12 Sep 2015
Posts: 4154
Re: In the figure, ABCD is a rectangle. The area of quadrilateral EBFD is  [#permalink]

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18 Mar 2019, 06:43
Top Contributor
Bunuel wrote:

In the figure, ABCD is a rectangle. The area of quadrilateral EBFD is one-half the area of the rectangle ABCD. Which one of the following is the value of AD ?

(A) 5

(B) 6

(C) 7

(D) 12

(E) 15

Attachment:
#GREpracticequestion In the figure, ABCD is a rectangle..jpg

APPROACH #2:

Let AB have length y

Area of rectangle ABCD = (base)(height) = xy

Since ABCD is a rectangle, we know that sides ED and BF are parallel
This means quadrilateral EBFD is a TRAPEZOID
Let y be the height of the trapezoid
This means ED and BF are the two bases of the trapezoid

Area of trapezoid = (base1 + base2)(height)/2
= (3 + 4)(y)/2
= 3.5y

The area of quadrilateral EBFD is one-half the area of the rectangle ABCD.
We can write: 3.5y = (1/2)xy
Multiply both sides by 2 to get: 7y = xy
Divide both sides by y to get: 7 = x

Which one of the following is the value of AD ?

Cheers,
Brent

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Re: In the figure, ABCD is a rectangle. The area of quadrilateral EBFD is   [#permalink] 18 Mar 2019, 06:43
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