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

Answer:

$z=\frac{15}{2}=7.5$

Step-by-step 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:

$\frac{AB}{EF}=\frac{AD}{EH}=\frac{BC}{FG}=\frac{DC}{HG}$

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

$\frac{BC}{FG}=\frac{DC}{HG}$

where:

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

we replace the values:

$\frac{8}{6}=\frac{10}{z}$

we solve for z

$z=\frac{10*6}{8}\\z=\frac{15}{2}\\ z=7.5$