Let x be the width of the original rectangle.

Then its length is (x+1), according to the condition,

    and the area is  x*(x+1).



The decreased dimensions are  (x-2) and ((x+1)-2) = (x-1),

so the decreased area is  (x-2)*(x-1).



From the condition,

    (x-2)*(x-1) = x*(x+1) - 30.


Simplify

    x^2 - 3x + 2 = x^2 + x - 30

        30 + 2   = x + 3x

          32     = 4x

          x      = 32/4 = 8.


ANSWER.  The original dimensions are  8 units (the width)  and  8+1 = 9 units (the length).