SOLUTION: A square room is 3m height and 10 litre is needed to paint all the walls and ceiling. If 1 litre of the paint will cover 16 square metres, write an equation and find the length of

Algebra ->  Surface-area -> SOLUTION: A square room is 3m height and 10 litre is needed to paint all the walls and ceiling. If 1 litre of the paint will cover 16 square metres, write an equation and find the length of       Log On


   

Question 850062: A square room is 3m height and 10 litre is needed to paint all the walls and ceiling. If 1 litre of the paint will cover 16 square metres, write an equation and find the length of the room.?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Total area to paint of the room ignoring windows or door: 3%2A3%2A5%2Am%5E2.
The description already specified, "square room"; all edges of this room are 3 meters.
Amount of paint to use: 3%2A3%2A5%2Am%5E2%281%2Aliter%2F%2816%2Am%5E2%29%29=%2845%2F16%29%2Aliters;
That was probably not what you wanted.

Maybe you are trying this:
The room is square around the floor, but this room is 3 meters high.
Let d = side length of the square shaped floor of this room. The total surface to be painted, the walls and the cieling, is 4%2A3%2Ad%2Bd%5E2=d%5E2%2B12d.
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The 10 liters of paint used means that, according to usage ratio, the area covered was 10%2Aliter%2816%2Am%5E2%29%2F%281%2Aliter%29=160%2Am%5E2 of surface.

Those two surface areas must be equal.
highlight_green%28d%5E2%2B12d=160%29.
Solve for d, which is as much the room length as it is the room width. (Remember, square room, at least for the floor and the cieling).
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160=2*5*4*4=20*8
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d%5E2%2B12d-160=0
%28d%2B20%29%28d-8%29=0
highlight%28highlight%28d=8%29%29------- Room length or width must be 8 meters.