To solve the problem of finding the width of the rectangular garden, given the perimeter $P = 43.8 \, \text{ft}$ and the length $L = 12.4 \, \text{ft}$, we can use the formula for the perimeter of a rectangle:

$P = 2L + 2W$

Where:

• $L$ is the length,
• $W$ is the width.

Step-by-step solution:

1. Substitute the given values into the perimeter equation:

$43.8 = 2(12.4) + 2W$

2. Simplify:

$43.8 = 24.8 + 2W$

3. Subtract 24.8 from both sides to isolate the term with $W$:

$43.8 - 24.8 = 2W$

$19 = 2W$

4. Divide both sides by 2 to find $W$:

$W = \frac{19}{2} = 9.5 \, \text{ft}$

Conclusion:

The width of the garden is $9.5 \, \text{ft}$.

Would you like further details or have any questions?

Here are 5 related questions for further exploration:

1. How do you calculate the area of the garden with the given dimensions?
2. What would the perimeter be if the length increased by 5 feet?
3. How does changing the width affect the perimeter of a rectangle?
4. What are the possible dimensions if the perimeter stays the same but the width increases?
5. Can you generalize the formula for the perimeter of other polygons?

Tip: Always double-check the values you substitute in a formula to avoid simple calculation errors.