Question

The polygons below are similar. Find the value of z.

Answer 1

The value of z is 8.

The two polygons are similar. Every length value for the polygon on the right is 2 units smaller than on the left. So, FG is 6, whereas BC is 8. Z is 8, whereas on the left is was 10. etc.

Answer 2

`z=(15)/(2)=7.5`

Explanation:

If the two polygons are similar it means their corresponding angles are congruent and the measures of their corresponding sides are proportional.

If the sides are proportional we can construct a relationship between them like this:

`(AB)/(EF)=(AD)/(EH)=(BC)/(FG)=(DC)/(HG)`

Using this relationships we can solve for z, more especifically if we use:

`(BC)/(FG)=(DC)/(HG)`

where:

`BC=8\\FG=6\\DC=10\\HG=z`

we replace the values:

`(8)/(6)=(10)/(z)`

we solve for z

`z=(10*6)/(8)\\z=(15)/(2)\\ z=7.5`