area of room is 320 and width is 4/5 of length
Area is w*l and \(w=\frac{4l}5\), thus the area is \(\frac{4l^2}5\). Make it equal to 320 and you get \(l^2=400\), thus \(l=\pm{20}\), the minus one not being meaningful in our context. Thus the length is 20, while the width is 16.