Question 775153
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 centimeters less than the original rectangle. Find the original dimensions.
<pre>
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.

{{{drawing(400,240,9,19,9,15,line(10,10,18,10),line(10,14,18,14),line(10,10,10,14),line(18,10,18,14),locate(14,10,2W), locate(18.2,12,W),
line(10,14,18,14),line(10,14,18,14) )}}}

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


{{{drawing(400,240,9,19,9,15,line(13,10,18,10),green(line(10,14,13,14)),line(13,14,18,14), green(line(10,10,13,10),line(10,14,13,14)),

green(locate(11.5,10,3)),locate(15.5,10,2W-3),locate(18.2,12,W),
line(13,10,13,14),green(line(10,10,10,14)),line(13,10,13,14),line(18,10,18,14),
green(line(10,14,13,14)),line(13,14,18,14),green(line(10,14,13,14)),line(13,14,18,14) )}}}{{{matrix(9,1,

leaving, just, this, resulting, rectangle,on,the,right,"----->")}}}{{{drawing(400,240,9,19,9,15,line(13,10,18,10),line(13,14,18,14),locate(15.5,10,2W-3),locate(18.2,12,W),
line(13,10,13,14),line(13,10,13,14),line(18,10,18,14),line(13,14,18,14),line(13,14,18,14) )}}}

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.

{{{drawing(400,240,9,19,9,15,green(line(10,14,13,14)),line(13,14,18,14), 

green(line(10,10,13,10),
line(10,11,13,11),line(10,12,13,12),line(10,12,13,12),line(10,13,13,13)),

line(13,10,18,10),locate(18.2,12,W=4),
line(13,11,18,11),line(13,12,18,12),line(13,12,18,12),line(13,13,18,13),
locate(14,10,2W-3=2(4)-3=5),
green(line(10,10,10,14),line(11,10,11,14),line(12,10,12,14)),line(13,10,13,14),line(14,10,14,14),line(15,10,15,14),line(16,10,16,14),line(17,10,17,14),line(18,10,18,14),green(locate(11.5,10,3))




 )}}}

Edwin</pre>