Of course! Let's solve the problem step-by-step.
1. Understand the given information:
- The perimeter of the rectangle is 96 meters.
- The length of the rectangle is 3 times its width.
2. Set up the formulas and variables:
- Let the width of the rectangle be [tex]\( w \)[/tex].
- According to the problem, the length will then be [tex]\( 3w \)[/tex].
3. Formula for the perimeter of a rectangle:
- The perimeter [tex]\( P \)[/tex] of a rectangle is given by the formula:
[tex]\[
P = 2 \times (\text{length} + \text{width})
\][/tex]
- Substitute the given perimeter and the expressions for length and width into the formula:
[tex]\[
96 = 2 \times (3w + w)
\][/tex]
4. Simplify the equation:
- Combine the terms inside the parentheses:
[tex]\[
96 = 2 \times 4w
\][/tex]
- This simplifies to:
[tex]\[
96 = 8w
\][/tex]
5. Solve for the width ( [tex]\( w \)[/tex] ):
- Divide both sides of the equation by 8:
[tex]\[
w = \frac{96}{8}
\][/tex]
[tex]\[
w = 12
\][/tex]
6. Find the length ( [tex]\( l \)[/tex] ):
- The length is 3 times the width:
[tex]\[
l = 3 \times w
\][/tex]
[tex]\[
l = 3 \times 12
\][/tex]
[tex]\[
l = 36
\][/tex]
7. Conclusion:
- The width of the rectangle is 12 meters.
- The length of the rectangle is 36 meters.
