Question

Find QP using given information in the figure.

Answer 1

$$\begin{gathered} \mathrm{In}△\mathrm{PNM}, \\ \frac{\mathrm{QM}}{\mathrm{QP}}=\frac{\mathrm{MN}}{\mathrm{PN}}\left(\mathrm{By}\mathrm{angle}\mathrm{bisector}\mathrm{theorem}\right) \\ \Rightarrow \frac{14}{\mathrm{QP}}=\frac{25}{40} \end{gathered}$$
$$\begin{gathered} \Rightarrow \mathrm{QP}=\frac{14\times 40}{25} \\ =22.4 \end{gathered}$$
Hence, the measure of QP is 22.4.