Let the breadth of the room be am
⇒ Length of the room=a+a2=3a2m
Area of the rooma×3a2=3a22sq.m
⇒ Cost of carpeting the room at Rs.3.25per sq.m=Rs.3.25×3a22
⇒75.50=3.25×3a22
⇒a2=175.50×23.25×3=36
⇒a=6
⇒ Breadth=a=6m and length=3×62=9m
Let the height of the room be hm
Area of 4 walls=2(l+b)×h=2(6+9)×h=30hsq.m
Area of 1 door and 2 windows=8sq.m
Area to be papered=Area of 4 walls−Area of 1 door and 2 windows
=(30h−8)sq.m
⇒Cost of papering walls at Rs.1.40per sq.m=Rs.(30h−8)×1.40
⇒240.80=(30h−8)×1.40
⇒30h−8=240.801.40=172
⇒30h=172+8=180
⇒h=18030=6m
Hence, dimensions of the room are
Length=9m, Breadth=6m and Height=6m