SOLUTION: I have no idea how to do this!!! please help!!!: The length of a rectangle is twice its width. If the length is decreased by 3 cm, the area of the resulting rectangle is 12 square

When you have a rectangle problem, always start out by drawing the rectangle.
We start with this rectangle. Label the width as W and the length as 2W.



Its area is (LENGTH)·(WIDTH) = (2W)·(W) = 2W²

We cut off the part in green below which is 3 centimeters chopped off 
the 2W length, making the length of the shorter black regtangle 2W-3




The resulting rectangle's area = (LENGTH)·(WIDTH) = (2W-3)·(W) = 2W²-3W

We are told that the area of the resulting rectangle is 12 square 
centimeters less than the original rectangle.

Area of resulting rectangle = Area of original rectangle - 12 square 
centimeters:

           2W²-3W = 2W² - 12
              -3W = -12
                W = 4 centimeters.

That's the width of both rectangles, since we did not change that.

The length of the original rectangle is 2W or 2(4) = 8 centimeters.

So you can see the actual square centimeters I will draw in the square
centimeters and you can see the 12 green square centimeters of area
that were cut off.



Edwin