The length of a rectangle is eight times it's width. if the length was decreased by 10 meters and the width decreased by 2 meters the area would be decreased by 162 m. find the original dimensions.

Alright, so l=8w (l=length, w=width, a=l*w or original area)

(l-10)*(w-20)=a-162

Substituting l for 8w and a for l*w and then 8w*w, we have
 (8w-10)(w-20)=8w^2-162=8w^2-160w-10w+200=8w^2-170w+200

8w^2-170w+200=8w^2-162 , so we subtract 8w^2 from both sides as well as subtract 200 to both to get -170w=-362, so w=362/170 and
 l= 8*362/170=2896/170