To find the perimeter of a rectangle when given the area and the width, we can follow these detailed steps:
1. Understand the Given Information:
- Area of the rectangle ([tex]\(A\)[/tex]) is [tex]\(18 \, \text{cm}^2\)[/tex].
- Width of the rectangle ([tex]\(W\)[/tex]) is [tex]\(2 \, \text{cm}\)[/tex].
2. Recall the Formula for Area:
The area ([tex]\(A\)[/tex]) of a rectangle is given by:
[tex]\[
A = \text{Length} \times \text{Width}
\][/tex]
3. Set Up the Equation:
Substituting the given values into the area formula, we get:
[tex]\[
18 = \text{Length} \times 2
\][/tex]
4. Solve for Length ([tex]\(L\)[/tex]):
[tex]\[
\text{Length} = \frac{18}{2} = 9 \, \text{cm}
\][/tex]
5. Recall the Formula for Perimeter:
The perimeter ([tex]\(P\)[/tex]) of a rectangle is given by:
[tex]\[
P = 2 \times (\text{Length} + \text{Width})
\][/tex]
6. Substitute the Length and Width into the Perimeter Formula:
Using the lengths we found, we have:
[tex]\[
P = 2 \times (9 \, \text{cm} + 2 \, \text{cm}) = 2 \times 11 \, \text{cm} = 22 \, \text{cm}
\][/tex]
7. Conclusion:
The perimeter of the rectangle is [tex]\(22 \, \text{cm}\)[/tex].
So, the length of the rectangle is [tex]\(9 \, \text{cm}\)[/tex] and the perimeter is [tex]\(22 \, \text{cm}\)[/tex].
