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
This is how i solved ... save way as Brent from GMATprepnow who is my teacher and he is awesome
but with my example
Let's say the sides of the square have length 4.
So, ∆ABD is a triangle with a base of length 4 and a height of length 4
So, area of ∆ABD = 1/2*4*4 = 8
Since , 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 2 and a height of length 2
So, area of ∆EFC = 1/2*2*2= 2
So, the TOTAL area of the 2 shaded regions = 8+ 2 = 10
Since the area of the SQUARE = (4)*(4) =16, and since the TOTAL area of the 2 shaded regions = 10, we can conclude that the area of the UNSHADED region = 16-10 = 6
What is the ratio of the shaded region area to unshaded region?
area of shaded region area/area of unshaded region = 10/6
We can create an EQUIVALENT ratio by multiplying top and bottom by 2 to get: 5/3, which is the same as 5 : 3