Question

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

its not 7.5!!! i just took the test and its wrong!!

Answer 2

Answer: The value of x = 16 units, y = 4.5 units and z = 7.5 units.

Explanation:

Since we have given that

ABCD and EFGH are two similar polygons.

Dimensions of ABCD are as follows :

AB = 6 units

BC = 8 units

AD = x units

CD = 10 units

Dimensions of EFGH are as follows :

EF = y

FG = 6 units

EH = 12 units

GH = z

Since they are similar:

`(AB)/(EF)=(BC)/(FG)=(CD)/(GH)=(AD)/(EH)\\\\(6)/(y)=(8)/(6)=\frac{10}z}=(x)/(12)`

First we take,

`(6)/(y)=(8)/(6)\\\\y=(36)/(8)\\\\y=4.5\ units`

similarly,

`(8)/(6)=(10)/(z)\\\\z=(60)/(8)\\\\z=7.5\ units`

similarly,

`(8)/(6)=(x)/(12)\\\\x=(96)/(6)\\\\x=16\ units`

Hence, the value of x = 16 units, y = 4.5 units and z = 7.5 units.