A rectangle 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