Question

If CX = 5 units, then DZ = ___ units

Answer 1

If CX = 5 units, then DZ = 4 units

Explanation:

From the figure, it can be seem that CD is parallel to XZ, therefore Triangle XYZ is similar to Triangle YCD.

Using the similarity condition, we have

`(XY)/(CY)=(ZY)/(YD)`

`(XC+CY)/(CY)= (ZD+DY)/(YD)`

Substituting the given values, we get

`(5+25)/(25)=(ZD+20)/(20)`

`(30)/(25)=(ZD+20)/(20)`

`(600)/(25)=ZD+20`

`24=ZD+20`

`ZD=4`

Thus, the value of ZD is 4 units.

Answer 2

`DZ=4\ units`

Explanation:

we know that

If CD is parallel to XZ

then

Triangle XYZ is similar to Triangle YCD

therefore

The ratio of their corresponding sides are equal

`(XY)/(CY)=(ZY)/(YD)`

we have

CX=5\ units, CY=25\ units, YD=20\ units,

`XY=CX+CY`

`XY=5+25=30\ units`

`ZY=YD+DZ`

`ZY=20+DZ`

substitute the values

`(30)/(25)=(20+DZ)/(20)`

`20(30)/(25)={20+DZ}`

`24={20+DZ}`

`DZ=4\ units`