Let's define the width of the rectangle as \( w \) centimeters. According to the problem, the length \( l \) is given by:
\[ l = 2w - 4 \]
The perimeter \( P \) of a rectangle is calculated using the formula:
\[ P = 2l + 2w \]
We know that the perimeter is 34 cm. Thus, we can set up the equation:
\[ 2l + 2w = 34 \]
We can simplify this equation to:
\[ l + w = 17 \]
Now, we have two equations:
- \( l = 2w - 4 \)
- \( l + w = 17 \)
Now, let's substitute the expression for \( l \) from the first equation into the second equation:
\[ (2w - 4) + w = 17 \]
Combining like terms gives us:
\[ 3w - 4 = 17 \]
Adding 4 to both sides:
\[ 3w = 21 \]
Dividing by 3:
\[ w = 7 \]
Now that we have the width, we can find the length using the first equation:
\[ l = 2(7) - 4 = 14 - 4 = 10 \]
So the dimensions of the rectangle are:
- Length = 10 cm
- Width = 7 cm
The correct answer is:
length = 10 cm; width = 7 cm.