x*(x+3)*((x+3)+5) = 198


    x*(x+3)*(x+8) = 198.


Method of the solution:


    a)  Trial and error,   

or

    b)  Factoring  the number 198 into the product of factors 

            198 = 3*6*11

        such that the second factor is 3 units greater than the first and the third factor

        is 5 units greater than the second.


The solution takes about 10 seconds.


Writing this post takes MUCH more time than that.



ANSWER.  3 units (the height);  6 units (the width)  and  11 units  (the length).