In triangle \( \Delta ABC \) with side lengths of 10, 12, and 8 inches, a midsegment connects the midpoints of two sides of the triangle and is parallel to the third side. The length of a midsegment is half the length of the side it is parallel to.
To find a possible midsegment length for a smaller triangle within \( \Delta ABC \):
- The longest side of \( \Delta ABC \) is 12 inches. The midsegment parallel to this side would therefore measure \( \frac{12}{2} = 6 \) inches.
- The midsegment parallel to the 10-inch side would measure \( \frac{10}{2} = 5 \) inches.
- The midsegment parallel to the 8-inch side would measure \( \frac{8}{2} = 4 \) inches.
Among the given response options, the only possible midsegment length that can be obtained is 6 inches.
Therefore, the answer is \( \boxed{6 \text{ inches}} \).
1 answer