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Use the formula [tex]P=2l+2w[/tex] to find the width of a rectangle when the length is 18 cm and the perimeter is 48 cm.

A. 15 cm
B. 30 cm
C. 6 cm
D. 12 cm


Sagot :

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]
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