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The length of a room is 3m longer than its width. A carpet whose area is #18m^2# is laid in the middle of the room leaving a margin 50cm wide between the wall and the carpet all around the room.
(a) Taking w to represent the width of the room, express the dimensions of the carpet in terms of w.
(b) Write down the area of the carpet in terms of w.
(c) Determine the dimensions of the room.
(d) The space between the wall and the carpet is covered with polythene material which costs sh.145 per square metre.
Find the cost of the material required.