Question

Find the value of X, Given that OP II NQ

Answer 1

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,

`(NM)/(OM)=(QM)/(PM)`

Plug the given values into the equation.

`(18)/(27)=(20)/(20+x)`

Cross-multiply and simplify to find x.

`\begin{gathered} 20+x=20\cdot(27)/(18) \\ =30 \\ x=30-20 \\ =10 \end{gathered}`

Hence the value of x is 10.