Question

The polygons below are similar. Find the value of z. Polygons ABCD and EFGH are shown. AB equals 6. BC equals 8. CD equals 10. AD equals x. EF equals y. FG equals 6. GH equals z. HE equals 12.

4.5
7.5
12
16

Answer 1

7.5

Explanation:

Look at the picture.

If polygons ABCD and EFGH are similar, then corresponding sides are in proportion.

`(GH)/(CD)=(FG)/(BC)`

We have

`GH=z,\ CD=10,\ FG=6,\ BC=8`

Substitute:

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

`8z=(10)(6)`

`8z=60` divide both sides by 8

`z=(60)/(8)\\\\z=7.5`