In ΔABC, it is given that AB = 9 cm, BC = 6 cm and CA = 7.5 cm. Also, ΔDEF is given such that EF = 8 cm and ΔDEF ~ ΔABC. Then, perimeter of ΔDEF is ______.

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In ΔABC, it is given that AB = 9 cm, BC = 6 cm and CA = 7.5 cm. Also, ΔDEF is given such that EF = 8 cm and ΔDEF ~ ΔABC. Then, perimeter of ΔDEF is 30 cm. Explanation: Because ΔDEF ~ ΔABC the vertex order gives D ↔ A, E ↔ B, F ↔ C, so EF corresponds to BC and corresponding sides are in the same ratio. Thus, scale factor k = (EF)/(BC) = $\frac{8}{6}$ = $\frac{4}{3}$ Perimeter of ABC = 9 + 6 + 7.5 = 22.5 cm Perimeter of DEF = k $\times$ 22.5 = $\frac{4}{3}$ xx 22.5 = 30 cm

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