Question

How to solve this the easiest way possible because I am confused

Answer 1

Provided that triangles POQ and RON are similar as shown below:

From the theorem of the similar triangle, we have

`(QP)/(RN)=(PO)/(RO)=(QO)/(NO)`

To find z, we have

`\begin{gathered} (6)/(z)=(10)/(5) \\ cross-multiply, \\ 10z=30 \\ divide\text{ both sides by the coefficient of z, which is 10} \\ (10z)/(10)=(30)/(10) \\ \Rightarrow z=3 \end{gathered}`

Hence, the value of z is

`3`