Question

What is the answer to this???

Answer 1

Option C.

Explanation:

It is given that each pair of polygon is similar.

From the given figure it is clear that,

`\angle E=\angle B=83^\circ`

`\angle F=\angle C=69^\circ`

`\angle G=\angle D=129^\circ`

`\angle H=\angle A=79^\circ`

Corresponding angles of similar figures are congruent. So,

`EFGH\sim BCDA`

Corresponding sides of similar figures are proportional.

`(GH)/(DA)=(HE)/(AB)`

`(6.4)/(3.2)=(9.6)/(4x)`

`2=(9.6)/(4x)`

`8x=9.6`

`x=1.2`

The value of x is 1.2 units.

`AB=4x=4(1.2)=4.8`

`CB=6x-2=6(1.2)-2=7.2-2=5.2`

Scale factor is

`k=(EF)/(BC)=(10.4)/(5.2)=2`

Therefore, the correct option is C.