Let the length of the rectangle be \( L \) and the width be \( W \). According to the problem, the length and width are in a ratio of 3:2, which we can express as:
\[ L = 3x \quad \text{and} \quad W = 2x \]
for some variable \( x \).
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2L + 2W \]
We know the perimeter is 100 meters, so we can set up the equation:
\[ 2L + 2W = 100 \]
Substituting the expressions for \( L \) and \( W \):
\[ 2(3x) + 2(2x) = 100 \]
Simplifying this:
\[ 6x + 4x = 100 \]
\[ 10x = 100 \]
Now, we solve for \( x \):
\[ x = 10 \]
Now we can find the length and width:
\[ L = 3x = 3(10) = 30 \text{ meters} \] \[ W = 2x = 2(10) = 20 \text{ meters} \]
Finally, the dimensions of the rectangle are:
\[ \text{length} = 30 \text{ meters} \] \[ \text{width} = 20 \text{ meters} \]