The given figure is a triangle. According to the triangle midsegment theorem,
midsegment = 1/2 * triangle base
From the diagram,
midsegment = 3x + 2
Base = 4x + 24
By applying the theorem, we have
3x + 2 = 1/2(4x + 24)
2(3x + 2) = 4x + 24
6x + 4 = 4x + 24
6x - 4x = 24 - 4
2x = 20
x = 20/2
x = 10
Thus,
midsegment = 3 * 10 + 2 = 30 + 2
Midsegment = 32
option D is correct
