Let the width of the rectangle be \( w \) meters. According to the problem, the length \( l \) can be expressed in terms of the width as follows:
\[ l = 2w + 3 \]
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2l + 2w \]
We know the perimeter is 30 meters, so we can set up the equation:
\[ 2l + 2w = 30 \]
Dividing the entire equation by 2 to simplify:
\[ l + w = 15 \]
Now, we can substitute the expression for \( l \) into this equation:
\[ (2w + 3) + w = 15 \]
Combining like terms:
\[ 3w + 3 = 15 \]
Next, we subtract 3 from both sides:
\[ 3w = 12 \]
Now, we divide by 3:
\[ w = 4 \]
Now that we have the width, we can find the length using the expression for \( l \):
\[ l = 2(4) + 3 = 8 + 3 = 11 \]
Thus, the length of the rectangle is:
\[ \boxed{11} \text{ meters} \]
To confirm, let's check the perimeter with these dimensions:
\[ P = 2l + 2w = 2(11) + 2(4) = 22 + 8 = 30 \text{ meters} \]
The calculations are consistent, confirming that the length is indeed \( \boxed{11} \) meters.
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