Question

In fig 2.37, $△$CAB$~$$△$FDE, find the values of m and n.

Answer 1

$$\begin{gathered} \mathrm{Here},△\mathrm{CAB}~△\mathrm{FDE} \\ \mathrm{By}\mathrm{similarity}\mathrm{correspondence},\mathrm{we}\mathrm{have}: \\ \frac{\mathrm{CA}}{\mathrm{FD}}=\frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{CB}}{\mathrm{FE}} \\ \Rightarrow \frac{13}{\mathrm{n}}=\frac{12}{\mathrm{m}}=\frac{5}{2}\left(\mathrm{Given}\right) \\ \Rightarrow \frac{13}{\mathrm{n}}=\frac{5}{2}\mathrm{and}\frac{12}{\mathrm{m}}=\frac{5}{2} \\ \Rightarrow \mathrm{n}=\frac{26}{5}\mathrm{and}\mathrm{m}=\frac{24}{5} \\ \Rightarrow \mathrm{n}=5.2\mathrm{and}\mathrm{m}=4.8 \end{gathered}$$