Question

In ∆LMN, ray MT bisects ∠LMN If LM = 6, MN = 10, TN = 8, then Find LT.

Answer 1

$$\begin{gathered} \mathrm{In}△\mathrm{LNM}, \\ \frac{\mathrm{LT}}{\mathrm{NT}}=\frac{\mathrm{LM}}{\mathrm{NM}}\left(\mathrm{By}\mathrm{angle}\mathrm{bisector}\mathrm{theorem}\right) \\ \Rightarrow \frac{\mathrm{LT}}{8}=\frac{6}{10} \end{gathered}$$
$$\begin{gathered} \Rightarrow \mathrm{LT}=\frac{8\times 6}{10} \\ =4.8 \end{gathered}$$
Hence, the measure of LT is 4.8.