Arectangle is four times as long as it is wide. if its length were diminished by 6 meters and its width were increased by 6 meters, it would be a square. what are its dimensions?

Let length be L and let wide be W
L=4*W
L decreased 6 to form a side of a sqaure, then: L-6
and W increased 6 to form the other side of a square, W+6
In a square both sides would be equals, so: L-6=W+6 and we have before L=4W so replace this L and we get:
 4W-6=W+6
Solve for W: 4W-W=6+6
                    3W=12
                    W=12/3=4
Now replace W into L=4W and we get L=4*4=16
Finally the dimensions for the rectangle are: Length=16 and Width=4

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