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In the figure, ABCD is a rectangle. The area of quadrilateral EBFD is
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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 ?
Re: In the figure, ABCD is a rectangle. The area of quadrilateral EBFD is
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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 ?
Re: In the figure, ABCD is a rectangle. The area of quadrilateral EBFD is
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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 ?
#GREpracticequestion In the figure, ABCD is a rectangle..jpg
APPROACH #2:
Let AD have length x 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 ? Since AD has length x, we know that AD = 7