Answer:width:5 centimeters
Length:10 centimeters
Explanation:To find the dimensions of the rectangle, let's denote the width of the rectangle as \( w \) centimeters. Given that the length is 5 centimeters longer than the width, the length can be represented as \( w + 5 \) centimeters.
The formula for the perimeter of a rectangle is given by:
\[ P = 2(\text{length} + \text{width}) \]
Substituting the given perimeter (30 centimeters) and the expressions for length and width, we get:
\[ 30 = 2(w + (w + 5)) \]
Simplifying the equation:
\[ 30 = 2(2w + 5) \]
\[ 30 = 4w + 10 \]
Subtract 10 from both sides:
\[ 20 = 4w \]
Divide both sides by 4:
\[ w = 5 \]
Now, we find the length by adding 5 centimeters to the width:
\[ \text{Length} = w + 5 = 5 + 5 = 10 \]
Therefore, the dimensions of the rectangle are:
- Width: 5 centimeters
- Length: 10 centimeters