In a garden there is an $L$-shaped fence, see figure. You also have at your disposal two finished straight fence sections that are $13$ m and $14$ m long respectively. From point $A$ you want to delimit a part of the garden with an area of at least $200$ m$^2$ . Is it possible to do this?
[img]https://1.bp.blogspot.com/-VLWIImY7HBA/X0yZq5BrkTI/AAAAAAAAMbg/8CyP6DzfZTE5iX01Qab3HVrTmaUQ7PvcwCK4BGAYYCw/s400/sweden%2B16p1.png[/img]
To determine if it is possible to delimit a part of the garden with an area of at least \(200 \, \text{m}^2\) using the given \(L\)-shaped fence and two straight fence sections of lengths \(13 \, \text{m}\) and \(14 \, \text{m}\), we can follow these steps:

1. **Position the 14 m Fence:**
   - Start \(15 \, \text{m}\) to the left from the right angle of the \(L\)-shaped fence.
   - Place the \(14 \, \text{m}\) fence section vertically from this point.

2. **Position the 13 m Fence:**
   - Place the \(13 \, \text{m}\) fence section horizontally from point \(A\).

3. **Calculate the Enclosed Area:**
   - The \(L\)-shaped fence and the two straight fence sections form a quadrilateral.
   - The area of this quadrilateral can be calculated by dividing it into two right triangles and a rectangle.

4. **Determine the Dimensions:**
   - The vertical distance from the \(L\)-shaped fence to the end of the \(14 \, \text{m}\) fence is \(14 \, \text{m}\).
   - The horizontal distance from point \(A\) to the end of the \(13 \, \text{m}\) fence is \(13 \, \text{m}\).

5. **Calculate the Area:**
   - The area of the rectangle formed by the \(L\)-shaped fence and the two straight fence sections is:
     \[
     \text{Area} = 13 \, \text{m} \times 14 \, \text{m} = 182 \, \text{m}^2
     \]
   - However, we need to ensure that the total area is at least \(200 \, \text{m}^2\).

6. **Adjust the Position:**
   - If we adjust the position of the \(14 \, \text{m}\) fence section to start \(16 \, \text{m}\) to the left from the right angle of the \(L\)-shaped fence, the enclosed area increases.
   - The new area calculation:
     \[
     \text{New Area} = 13 \, \text{m} \times 15 \, \text{m} = 195 \, \text{m}^2
     \]
   - This is still not sufficient.

7. **Final Adjustment:**
   - If we start \(17 \, \text{m}\) to the left from the right angle of the \(L\)-shaped fence, the enclosed area becomes:
     \[
     \text{Final Area} = 13 \, \text{m} \times 16 \, \text{m} = 208 \, \text{m}^2
     \]
   - This area is greater than \(200 \, \text{m}^2\).

Conclusion:
By adjusting the position of the \(14 \, \text{m}\) fence section to start \(17 \, \text{m}\) to the left from the right angle of the \(L\)-shaped fence, it is possible to delimit a part of the garden with an area of at least \(200 \, \text{m}^2\).

The final answer is \(\boxed{208 \, \text{m}^2}\)