Question

If $△$ABC $~$ $△$DEF and AB = 12 cm, BC =8, AC = 15, DE = 18, then find EF and DF.

Answer 1

$$\begin{gathered} \mathrm{Here},△\mathrm{ABC}~△\mathrm{DEF} \\ \mathrm{By}\mathrm{similarity}\mathrm{correspondence},\mathrm{we}\mathrm{have}: \\ \frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{BC}}{\mathrm{EF}}=\frac{\mathrm{AC}}{\mathrm{DF}} \\ \Rightarrow \frac{12}{18}=\frac{8}{\mathrm{EF}}=\frac{15}{\mathrm{DF}} \\ \Rightarrow \frac{2}{3}=\frac{8}{\mathrm{EF}}=\frac{15}{\mathrm{DF}} \\ \Rightarrow \frac{2}{3}=\frac{8}{\mathrm{EF}}\mathrm{and}\frac{2}{3}=\frac{15}{\mathrm{DF}} \\ \Rightarrow \mathrm{EF}=12\mathrm{and}\mathrm{DF}=22.5 \end{gathered}$$