To find the width of a rectangle given the length and the perimeter, we can start by using the formula for the perimeter of a rectangle:
[tex]\[ P = 2l + 2w \][/tex]
Where:
- [tex]\( P \)[/tex] is the perimeter
- [tex]\( l \)[/tex] is the length
- [tex]\( w \)[/tex] is the width
We are given the length [tex]\( l = 18 \)[/tex] cm and the perimeter [tex]\( P = 48 \)[/tex] cm. We need to find the width [tex]\( w \)[/tex].
Step-by-Step Solution:
1. Substitute the given values for the perimeter and the length into the perimeter formula:
[tex]\[ 48 = 2(18) + 2w \][/tex]
2. Simplify the equation:
[tex]\[ 48 = 36 + 2w \][/tex]
3. Isolate the term containing [tex]\( w \)[/tex] by subtracting 36 from both sides:
[tex]\[ 48 - 36 = 2w \][/tex]
[tex]\[ 12 = 2w \][/tex]
4. Solve for [tex]\( w \)[/tex] by dividing both sides by 2:
[tex]\[ w = \frac{12}{2} \][/tex]
[tex]\[ w = 6 \][/tex]
So, the width of the rectangle is [tex]\( 6 \)[/tex] cm.
Given the options (15 cm, 30 cm, 6 cm, 12 cm), the correct answer is:
[tex]\[ 6 \text{ cm} \][/tex]
