Answer:
FG = 25.6
Explanation:
ABC to DEC = 5:2
DEC to FEG = 1:4
so,
ABC to FEG = 5/2 × 1/4 = 5:8
that means the scaling factor from small to large is 8/5.
therefore,
EG = BC × 8/5 = 10×8/5 = 2×8 = 16
the side length ratio for ABC tells us
AB:BC:AC = 5 : 2 1/2 : 4
BC = 10
so,
AB:BC = 5 : 2 1/2 = 5 : 2.5
AB:10 = 5 : 2.5
2.5AB = 50
AB = 50/2.5 = 20
AC:AB = 4:5
AC:20 = 4:5
AC = 20×4/5 = 80/5 = 16
FG = AC × 8/5 = 16 × 8/5 = 128/5 = 25.6