The value of x is 13.
In a triangle with midsegment DE, DE is parallel to and half the length of the third side (BC). The midsegment theorem states that the midsegment of a triangle is parallel to one side and half its length. In this case, DE is parallel to BC and has a length of x, while BC has a length of 26.
Using the midsegment theorem, we can set up the following relationship:
x = 13
Therefore, the value of x is 13. The midsegment DE is half the length of BC, making it 13 units in this triangle. This relationship holds true for any triangle with a midsegment, providing a useful method for determining segment lengths in triangles.