the living room is rectangle with length l and width w

the width is twice the length

w = 2l

the area of the living room is 162 ft^2

l*w = 162

plug w = 2l into the last equation

l*2l = 162 divide both sides by 2

l^2 = 81

l = 9 ft

w = 2*9

w = 18 ft

the dimensions of the room are 9 ft and 18 ft.