Question

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

Answer 1

Solution:

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

From the theorem of the similar triangle, we have

$\frac{QP}{RN}=\frac{PO}{RO}=\frac{QO}{NO}$

To find z, we have

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

Hence, the value of z is

$3$