Sure! Let's solve the problem step-by-step:
### Given:
- The area of the rectangle [tex]\( A = 72 \)[/tex] mm²
- The length of the rectangle [tex]\( l = 8 \)[/tex] mm
### To Find:
- The perimeter of the rectangle, [tex]\( P \)[/tex]
### Steps:
1. Determine the width of the rectangle ([tex]\( w \)[/tex]):
We know the area of the rectangle is given by the formula:
[tex]\[
A = l \times w
\][/tex]
We can rearrange this formula to solve for the width ([tex]\( w \)[/tex]):
[tex]\[
w = \frac{A}{l}
\][/tex]
Plugging in the given values:
[tex]\[
w = \frac{72 \, \text{mm}^2}{8 \, \text{mm}} = 9 \, \text{mm}
\][/tex]
2. Calculate the perimeter ([tex]\( P \)[/tex]):
The formula for the perimeter of a rectangle is:
[tex]\[
P = 2 \times (l + w)
\][/tex]
Substituting in the values for length and width:
[tex]\[
P = 2 \times (8 \, \text{mm} + 9 \, \text{mm})
\][/tex]
Simplify the expression inside the parentheses:
[tex]\[
P = 2 \times 17 \, \text{mm}
\][/tex]
Finally, perform the multiplication:
[tex]\[
P = 34 \, \text{mm}
\][/tex]
### Answer:
The perimeter of the rectangle is 34 mm.
