The length of a rectangle is 17 centimeters less than four times its width. its area is 42 square centimeters. find the dimensions of the rectangle.

Let w=width and l=length. 
so, we know that 4xwidth(w) - 17 = length(l) 
so, 4w-17=l 
we also know that area (l x w) = 42 

As l=4w-17w x (4w-17) = 42 
Hence, 4w^2 -17w-42=0 

Be factorising this, we get (4w+7)x(w-6) = 0 
So, by using null factor law, w=6 or w=-7/4 
But, as width must be positive, w = 6 

Now, sub w=6 into the formula we found earlier, l=4w-17 
l=4(6)-17 = 7 

Hence, Length = 7 and Width = 6