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

How to solve this the easiest way possible because I am confused-example-1

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5 votes

Solution:

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


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How to solve this the easiest way possible because I am confused-example-1
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