Let's denote the width of the rectangle as \( w \) (in centimeters). According to the problem, the length \( l \) can be expressed in terms of the width as follows:
\[ l = 2w - 4 \]
The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2l + 2w \]
Given that the perimeter is 34 cm, we can set up the equation:
\[ 2l + 2w = 34 \]
We can simplify this equation by dividing everything by 2:
\[ l + w = 17 \]
Now we have a system of two equations:
- \( l = 2w - 4 \)
- \( l + w = 17 \)
Next, we can substitute the expression for \( l \) from the first equation into the second equation:
\[ (2w - 4) + w = 17 \]
Combining the \( w \) terms gives us:
\[ 3w - 4 = 17 \]
Now, we can solve for \( w \):
\[ 3w = 17 + 4 \] \[ 3w = 21 \] \[ w = 7 \]
Now that we have the width, we can find the length using the expression for \( l \):
\[ l = 2w - 4 = 2(7) - 4 = 14 - 4 = 10 \]
Thus, the dimensions of the rectangle are:
- Width: \( 7 \) cm
- Length: \( 10 \) cm
To conclude, the dimensions of the rectangle are:
\[ \text{Width} = 7 , \text{cm}, \quad \text{Length} = 10 , \text{cm} \]