In this problem, the length is compared to the width of the rectangle. So let's assign a variable that represents the width of the rectangle.

Let the width be w.

`width = w`

Since the length is 2 meters more than twice its width, the expression that represent it...

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In this problem, the length is compared to the width of the rectangle. So let's assign a variable that represents the width of the rectangle.

Let the width be w.

`width = w`

Since the length is 2 meters more than twice its width, the expression that represent it is:

`l e n g t h = 2w + 2`

Then, plug-in the length and width to the formula of perimeter of rectangle.

`P = 2*l e n g th + 2*width`

`P=2(2w+2)+2*w`

Plug-in too the given perimeter of the rectangle.

`46=2(2w+2)+2*w`

Then, solve for w.

`46=4w+4+2w`

`46=6w+4`

`42=6w`

`7=w`

So, the width of the rectangle is 7 meters.

Then, plug-in the value of w to the expression that represents the length.

`l e n g t h = 2w + 2`

`l e n g t h = 2(7) + 2`

`l e n g t h = 14 + 2`

`l e n g t h = 16`

**Therefore, the length of the rectangle is 16 meters.**