This was a far better explanation .
Obviously there has to be a logic while considering l=2b or l=2&b=1
kstv explains it in the right way

kstv wrote:2) The 3 small rectangle have same dimension or L1*B1
Let Dimesion of LMNK be L*B
Area of LMNK = 3 times the small rect KN
L*B = 3 L1*B1
MN*KN = 3 KN*B1
MN = 3 B1
MN-B1 = KN
KN = 2 B1
KN/MN=2/3
Suff

i still don't get it..sorry im so slow on this one.

let KN=2,then LK can equal to 6, the demention of each of the three little one could still be 4, and KN/MN=1/3
let KN=2,then LK can equal to 3, the demention of each of the three little one could still be 2, and KN/MN=2/3

I think many guyz are suffering from choice B. I just re-numbering original picture.

Here you are


Right! we can't just know the fact that "aM" is same withe "bN" and "ac = 2cb" !!!!
Rather, we should calculate the area of three rectangles!!

My solution]
Lets say "aM = x" and "ac=y"
According B), We know the area & perimeter of rectangle acbM are same with those of dKnb. So,
bn= y-x and we can make following equation.
xy=2x(y-x)
xy=2xy-2x2
xy-2x2=0
x(y-2x)=0
So, now we can know y=2x.

Then, we can now say kn=2x / MN=3x so 2/3