Question

In ∆MNP, NQ is a bisector of ∠N. If MN = 5, PN = 7 MQ = 2.5 then Find QP.

Answer 1

$$\begin{gathered} \mathrm{In}△\mathrm{PNM}, \\ \frac{\mathrm{QM}}{\mathrm{QP}}=\frac{\mathrm{MN}}{\mathrm{PN}}\left(\mathrm{By}\mathrm{angle}\mathrm{bisector}\mathrm{theorem}\right) \\ \Rightarrow \frac{2.5}{\mathrm{QP}}=\frac{5}{7} \end{gathered}$$
$$\begin{gathered} \Rightarrow \mathrm{QP}=\frac{2.5\times 7}{5} \\ =3.5 \end{gathered}$$
Hence, the measure of QP is 3.5.