I have a feeling that this question has been answered before, but here goes:

Notice that the perimeter = 2(length + width).

Now, let's break each one of those based on our rectangles.
The length is the sum of diagonals and since the squares are identical, the length will be 2*diagonal. Say the side of a small square is x. This makes the diagonal x*sqrt(2) (it's that formula for the diagonal of a square), so the length of the rectangle will be 2x*sqrt(2).

On the other hand, the width is just one diagonal long, so width = x*sqrt(2).

The perimeter will be 18sqrt(2) = 2(x*sqrt(2) + 2x*sqrt(2)).

9sqrt(2) = 3xsqrt(2)

x = 3. Since the squares have sides of 3 each, the perimeter will be 4*3 = 12.

I got the answer as 6. DanaJ - from the problem, i read the perimeter of the rectangle as 18/sqrt(2). You have assumed 18*sqrt(2).

18/sqrt(2) = 2(x*sqrt(2) + 2x*sqrt(2))

So if i change your equation as above, x works out to as 1.5 and perimeter as 6.

thanks for ur responses.....