Let's solve the given problem step-by-step:
1. Calculate the Width:
- We know the formula for the area of a rectangle is:
[tex]\[
\text{Area} = \text{Length} \times \text{Width}
\][/tex]
- We're given the area (72 square centimeters) and the length (12 centimeters). We need to find the width.
- Rearranging the formula to solve for the width:
[tex]\[
\text{Width} = \frac{\text{Area}}{\text{Length}}
\][/tex]
- Plugging in the given values:
[tex]\[
\text{Width} = \frac{72}{12}
\][/tex]
- Therefore, the width is:
[tex]\[
\text{Width} = 6 \text{ centimeters}
\][/tex]
2. Calculate the Perimeter:
- We know the formula for the perimeter of a rectangle is:
[tex]\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width})
\][/tex]
- We already know the length (12 centimeters) and we just calculated the width (6 centimeters).
- Plugging in these values:
[tex]\[
\text{Perimeter} = 2 \times (12 + 6)
\][/tex]
- Simplifying inside the parentheses first:
[tex]\[
\text{Perimeter} = 2 \times 18
\][/tex]
- Therefore, the perimeter is:
[tex]\[
\text{Perimeter} = 36 \text{ centimeters}
\][/tex]
So, the width of the rectangle is 6 centimeters, and the perimeter is 36 centimeters.
