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



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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

Answer: C

Cheers,
Brent

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