Answer:
Option C.
Step-by-step explanation:
It is given that each pair of polygon is similar.
From the given figure it is clear that,
[tex]\angle E=\angle B=83^\circ[/tex]
[tex]\angle F=\angle C=69^\circ[/tex]
[tex]\angle G=\angle D=129^\circ[/tex]
[tex]\angle H=\angle A=79^\circ[/tex]
Corresponding angles of similar figures are congruent. So,
[tex]EFGH\sim BCDA[/tex]
Corresponding sides of similar figures are proportional.
[tex]\dfrac{GH}{DA}=\dfrac{HE}{AB}[/tex]
[tex]\dfrac{6.4}{3.2}=\dfrac{9.6}{4x}[/tex]
[tex]2=\dfrac{9.6}{4x}[/tex]
[tex]8x=9.6[/tex]
[tex]x=1.2[/tex]
The value of x is 1.2 units.
[tex]AB=4x=4(1.2)=4.8[/tex]
[tex]CB=6x-2=6(1.2)-2=7.2-2=5.2[/tex]
Scale factor is
[tex]k=\dfrac{EF}{BC}=\dfrac{10.4}{5.2}=2[/tex]
Therefore, the correct option is C.
