To find the dimensions of the rectangle, let's denote the width as \( w \) centimeters. According to the problem, the length \( l \) can be expressed as:
\[ l = 2w - 3 \]
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2l + 2w \]
We know the perimeter is 48 cm, so we can set up the equation:
\[ 2l + 2w = 48 \]
Substituting the expression for \( l \):
\[ 2(2w - 3) + 2w = 48 \]
Now, let's simplify the equation:
\[ 4w - 6 + 2w = 48 \]
Combine like terms:
\[ 6w - 6 = 48 \]
Now, add 6 to both sides:
\[ 6w = 54 \]
Dividing both sides by 6 gives:
\[ w = 9 \]
Now substitute back to find the length:
\[ l = 2(9) - 3 = 18 - 3 = 15 \]
So, the dimensions of the rectangle are:
- Length = 15 cm
- Width = 9 cm
From your provided options, the solution corresponds to:
length = 15 cm; width = 9 cm.