Let's make "x" the width.
Length = x-12.
Area of rectangle: Width * Length.
This means: x(x-12) = 85.
Simplifying that is: x^2 - 12x = 85.
Rearranging it: x^2 - 12x - 85 = 0.
Factor it: (x+5)(x+17)-85 = 0
We can set both factors to 0 and solve for x:
x = -5 which doesn't work
x = 17 which works.
And for the Length: x - 12 = 17 -12 = 5.
I used the same method as CPhill though...