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We are given with an isosceles triangle with 8 units on two sides and 6 units on one side. The midpoint connecting two sides is called the mid-segment. The mid-segment is calculated using the law of cosines. Angle ABC is equal to 67.98 degrees. Using this angle, we compute the mid-segment using half of the other sides. The length is equal to 4 units. 

ABC is isosceles with AB=AC=8 units and BC=6 units.

ABC is a bigger triangle with AB = AC = 8  and BC = 6

Smaller triangle BDE is formed by connecting D and E that are midpoints of AB and BC respectively. D is the midpoint. AB =8 so AD = 4. Also BE = 4

Triangles ABC  and BDE are similar triangles. so we make a proportion

[tex] \frac{DE}{AC} =\frac{BD}{AB}=\frac{BE}{BC}[/tex]

[tex] \frac{DE}{8} =\frac{4}{8}=\frac{3}{6} [/tex]

[tex] \frac{DE}{8} =\frac{4}{8} [/tex]

DE= 4  

The length of DE = 4 units


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