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 the perimeter of ΔDEF is:

1. 22.5 cm

2. 25 cm

3. 27 cm

4. 30 cm

Given,

ΔDEF ∼ ΔABC

Perimeter of ΔABC = AB + BC + CA = 9 + 6 + 7.5 = 22.5 cm.

Since the triangles are similar,

$\therefore \dfrac{\text{Perimeter of ΔABC}}{\text{Perimeter of ΔDEF}} = \dfrac{BC}{EF} \\[1em] \Rightarrow \dfrac{22.5}{\text{Perimeter of ΔDEF}} = \dfrac{6}{8} \\[1em] \Rightarrow \text{Perimeter of ΔDEF} = \dfrac{22.5 \times 8}{6} \\[1em] \Rightarrow \text{Perimeter of ΔDEF} = \dfrac{180}{6} \\[1em] \Rightarrow \text{Perimeter of ΔDEF} = 30 \text{ cm.}$

Hence, option 4 is the correct option.