To find a possible midsegment length of a smaller triangle that is similar (congruent) to triangle \( \Delta ABC \) with side lengths of 10, 12, and 8 inches, we use the property of midsegments in triangles.
A midsegment connects the midpoints of two sides of a triangle, and it is parallel to the third side. The length of a midsegment is equal to half the length of the third side.
In triangle \( \Delta ABC \), we can identify the lengths of the sides:
- Side AB: 10 inches
- Side BC: 12 inches
- Side CA: 8 inches
The midsegment lengths for each pair of sides would be:
- Midsegment parallel to side BC (12 inches): Length = 12 / 2 = 6 inches
- Midsegment parallel to side CA (8 inches): Length = 8 / 2 = 4 inches
- Midsegment parallel to side AB (10 inches): Length = 10 / 2 = 5 inches
Among the given responses, the possible midsegment length of the smaller triangle that can be formed within \( \Delta ABC \) is:
6 inches
So the correct answer is 6 inches.