the area of a rectangular room is 65 m^2. Find the perimeter of the room given that its length is 3 m more than thrice its width

Hmmm. If you had said three more than twice its width, I'd have immediately said the room was 5x13. But, now we have to use some algebra.

w(3w+3) = 65
w = 4.1815

for the perimeter, we want 2(w+3w+3)=39.452