To solve the problem, we note that DE is a midsegment of triangle $\triangle ABC$. A midsegment in a triangle has two properties:

1. It is parallel to the third side of the triangle.
2. Its length is half the length of the third side.

From the image:

• $DE = 58$, and it is the midsegment.
• The side $BC$ is the third side.

Step-by-Step Solution:

Since $DE$ is a midsegment: $DE = \frac{1}{2} BC$

Substituting $DE = 58$: $58 = \frac{1}{2} BC$

Multiply through by 2: $BC = 2 \cdot 58 = 116$

Thus, the value of $x$, which is equal to $BC$, is: $x = 116$

Final Answer:

$x = 116$

Would you like further details or clarifications? 😊

Related Questions:

1. What are the properties of midsegments in a triangle?
2. How does the midsegment theorem apply in coordinate geometry?
3. If one midsegment is given, how can the triangle’s perimeter be calculated?
4. How can you determine the midsegment's length in an isosceles triangle?
5. How do you verify if a segment is truly a midsegment in a triangle?

Tip:

When working with midsegments, always check if the segment connects the midpoints of two sides to confirm it follows the midsegment theorem.