The shaded region in the figure above represents a rectangular frame with length 18 inches and width 15 inches. The frame encloses a rectangular picture that has the same area as the frame itself. If the length and width of the picture have the same ratio as the length and width of the frame, what is the length of the picture, in inches?
9~$\sqrt{2}$~
3~$\sqrt{2}$~
~$\frac{9}{\sqrt{2}}$~
15(1-~$\frac{1}{\sqrt{2}}$~ )
9/2
设白色部分的边长为18k 和15k
18k * 15k * 2 = 18*15
k = √2/2
18k = 9√2
设长为X宽为Y
X/Y = 18/15
18*15 = 2*X*Y
X = 9√2