Bunuel wrote:
ABCD is a square. E and F are the midpoints of sides CD and BC, respectively. What is the ratio of the shaded region area to the unshaded region?
A. 1:1
B. 2:1
C. 3:1
D. 5:3
E. 8:3
Another approach is to
assign some nice values to the diagram.
Let's say the sides of the square have length 2.
So, ∆ABD is a right triangle with a base of length 2 and a height of length 2
So, area of
∆ABD = (2)(2)/2 = 2Since , E and F are the midpoints of sides CD and BC, respectively, we know that ∆EFC is a right triangle with a base of length 1 and a height of length 1
So, area of
∆EFC = (1)(1)/2 = 0.5So, the TOTAL area of the 2 shaded regions =
2 +
0.5 =
2.5Since the area of the SQUARE = (2)(2) =4, and since the TOTAL area of the 2 shaded regions =
2.5, we can conclude that the area of the UNSHADED region = 4 -
2.5 =
1.5What is the ratio of the shaded region area to unshaded region?area of shaded region area/
area of unshaded region =
2.5/
1.5We can create an EQUIVALENT ratio by multiplying top and bottom by 2 to get:
5/
3, which is the same as
5 :
3Answer: D
Cheers,
Brent
_________________
Test confidently with gmatprepnow.com