You start by taking the area of the border of the frame 18*15=270

Then you subtract that number by inner section of the frame. Let's call it L*W

So the area of the frame itself would be 270-L*W

Now, it's stated that the picture has the same area of the frame itself which means 270-L*W=L*W

By simplifying, you will get: 135=L*W

Since this equation has two unknowns there must be an addition equation to complete this problem.

The last sentences points out the length and width of the picture has the same ratio as the length and width of the frame.

Which means this: (L/W)=18/15

Now you solve for L

Let's take (L/W)=18/15 first, W=15L/18=5L/6

135=L*(5L/6)
[(6*135)/5]=L^2
(6*27)=L^2
(6*3*9)=L^2
(18*9)=L^2
(2*9*9)=L^2

Take the square root of both 9s and 2.

And you will get 9*Sqrt(2)=L <---The answer