Answer:
FG = 31
Step-by-step explanation:
By applying mid-segment theorem in the given trapezoid,
Segment joining midpoints of the nonparallel sides is parallel and measure the half of the sum of parallel sides.
FG = [tex]\frac{1}{2}[UV+TW][/tex]
(7x - 4) = [tex]\frac{1}{2}[(6x-6)+38][/tex]
2(7x - 4) = 6x + 32
14x - 8 = 6x + 32
14x - 6x = 32 + 8
8x = 40
x = 5
Therefore, FG = (7x - 4)
= 7(5) - 4
= 31
