Answer: The larger piece is 16 inches
Step-by-step explanation: Median of a triangle is a line segment uniting a vertex and the midpoint of the opposite side. A triangle has 3 medians and the point where these 3 intersect is called centroid.
The ratio of one median is 2:1, which means the line segment is divides by the centroid into two parts, one the double of the other. So:
2x + x = 24
3x = 24
x = 8
Then, the larger piece is
2x = 2(8) = 16
The larger part of the median measuring 24 inches is 16 inches