To find the length and width of the rectangle, we can use the information given about the ratio and the perimeter.
Let the length be \( 5x \) and the width be \( 3x \), where \( x \) is a common factor.
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2(\text{length} + \text{width}) \]
Substituting the length and width in terms of \( x \):
\[ 32 = 2(5x + 3x) \]
Simplifying inside the parentheses:
\[ 32 = 2(8x) \]
This simplifies to:
\[ 32 = 16x \]
Now, solving for \( x \):
\[ x = \frac{32}{16} = 2 \]
Now we can find the length and width:
- Length: \( 5x = 5 \times 2 = 10 \) millimeters
- Width: \( 3x = 3 \times 2 = 6 \) millimeters
Therefore, the dimensions of the rectangle are:
Length = 10 millimeters
Width = 6 millimeters
1 answer