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

Given △ABC ~ △DEF, so

$\therefore \dfrac{AB}{DE} = \dfrac{AC}{DF} = \dfrac{BC}{EF} \\[1em] \text{Consider, } \dfrac{AB}{DE} = \dfrac{AC}{DF} \\[1em] \dfrac{4}{6} = \dfrac{AC}{12} \\[1em] AC = \dfrac{48}{6} \\[1em] AC = 8.$

Now consider,

$\dfrac{AB}{DE} = \dfrac{BC}{EF} \\[1em] \dfrac{4}{6} = \dfrac{BC}{9} \\[1em] BC = \dfrac{36}{6} \\[1em] BC = 6$

Perimeter of △ABC = AB + BC + AC = 4 + 6 + 8 = 18 cm.

Hence, perimeter of △ABC = 18 cm.