Question

If ∆ABC ~ ∆DEF, AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, then the perimeter of ∆ABC is __________.

Answer 1

∆ABC ~ ∆DEF (Given)

$\therefore \frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{BC}}{\mathrm{EF}}=\frac{\mathrm{CA}}{\mathrm{FD}}$ (If two triangles are similar, then the ratio of their corresponding sides is proportional)

$$\begin{gathered} \Rightarrow \frac{4\mathrm{cm}}{6\mathrm{cm}}=\frac{\mathrm{BC}}{9\mathrm{cm}}=\frac{\mathrm{CA}}{12\mathrm{cm}} \\ \Rightarrow \frac{\mathrm{BC}}{9\mathrm{cm}}=\frac{2}{3}\mathrm{and}\frac{\mathrm{CA}}{12\mathrm{cm}}=\frac{2}{3} \\ \Rightarrow \mathrm{BC}=\frac{2\times 9}{3}=6\mathrm{cm}\mathrm{and}\mathrm{CA}=\frac{2\times 12}{3}=8\mathrm{cm} \end{gathered}$$

∴ Perimeter of ∆ABC = AB + BC + CA = 4 cm + 6 cm + 8 cm = 18 cm

If ∆ABC ~ ∆DEF, AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, then the perimeter of ∆ABC is ___18 cm___.