Given that:
ON = 9, PQ = x, OP = y, NM = 18, QM = 20
From the figure, the triangles OPM and NQM are similar. Hence their sides are proportional, that is,
[tex]\frac{NM}{OM}=\frac{QM}{PM}[/tex]
Plug the given values into the equation.
[tex]\frac{18}{27}=\frac{20}{20+x}[/tex]
Cross-multiply and simplify to find x.
[tex]\begin{gathered} 20+x=20\cdot\frac{27}{18} \\ =30 \\ x=30-20 \\ =10 \end{gathered}[/tex]
Hence the value of x is 10.
