Area of Picture and the Rectangular Frame is same.
and the area of the entire reagion is 18in * 15in = 270in

So area of the Picture is 270in / 2 = 135 in.

now the ratio is 15:18 i.e 5:6

So 5x * 6x = 135
30x^2 = 135
x^2 = 135 / 30
x^2 = 4.5
x^2 = 9/2
x = 3/root2

now lenght = 6x
= 6 * 3 / root 2
= 9 root 2

Ans A.

IMO A

Suppose length of pic = x, width of pic = y

x/y=18/15 ------(1)

area of pic = xy

area of frame = 18*15-xy

Now, the question says 18*15-xy = xy => 2xy = 18*15 => xy = 9*15 ----(2)

Solve (1) and (2) to get x = 9root2

Equation1: 18/15 = a/b;  b = 15 x a/18

Equation2: Area (Outer Rectangle) = Area (Frame) + Area (Inner Rectangle)

But; Area (Frame) = Area (Inner Rectangle)

Area (Outer Rectangle) = 2 x Area (Inner Rectangle)

18 x 5 = 2 x a x b (a & b side of inner rect.)

Equating the value of b; a = 9 root(2)

Answer is A

Thanks guys. It makes sense now.