Question

In ∆ABC, it is given that AB = 9 cm, BC = 6 cm and CA = 7.5 cm. Also, in ∆DEF , EF = 8 cm and ∆DEF ∼ ∆ABC. Then, perimeter of ∆DEF is
(a) 22.5 cm
(b) 25 cm
(c) 27 cm
(d) 30 cm

Answer 1

(d) 30 cm

Perimeter of $△$ABC = AB + BC + CA = 9 + 6 + 7.5 = 22.5 cm

$\because$ ∆DEF ∼ ∆ABC

$$\begin{gathered} \therefore \frac{\mathrm{Perimeter}△\left(ABC\right)}{\mathrm{Perimeter}(△DEF)}=\frac{BC}{EF} \\ \Rightarrow \frac{22.5}{\mathrm{Perimeter}(△DEF)}=\frac{6}{8} \\ \Rightarrow \mathrm{Perimeter}(△DEF)=\frac{22.5\times 8}{6}=30\mathrm{cm} \end{gathered}$$