To find a possible midsegment length of a smaller triangle within triangle \( \Delta ABC \) with side lengths of 10, 12, and 8 inches, we need to remember that a midsegment of a triangle is parallel to one side and its length is half the length of that side.
The side lengths of triangle \( \Delta ABC \) are:
- 10 inches
- 12 inches
- 8 inches
The midsegments corresponding to these sides would be:
- For the 10-inch side, the midsegment would be \( \frac{10}{2} = 5 \) inches.
- For the 12-inch side, the midsegment would be \( \frac{12}{2} = 6 \) inches.
- For the 8-inch side, the midsegment would be \( \frac{8}{2} = 4 \) inches.
The possible midsegment lengths from the options provided are:
- 10 inches (not possible since it's larger than any side length)
- 16 inches (not possible since it's larger than any side length)
- 6 inches (possible, as it's half the length of the 12-inch side)
- 8 inches (not possible, as it's not half any side)
Given these evaluations, the possible midsegment length of the smaller triangle that can be drawn congruently within triangle \( \Delta ABC \) is 6 inches.