Question

∆ABC ∼ ∆DEF such that AB = 9.1 cm and DE = 6.5 cm. If the perimeter of ∆DEF is 25 cm, what is the perimeter of ∆ABC?
(a) 35 cm
(b) 28 cm
(c) 42 cm
(d) 40 cm

Answer 1

(a) 35 cm

$\because$ ∆ABC ∼ ∆DEF

$$\begin{gathered} \therefore \frac{\mathrm{Perimeter}(△ABC)}{\mathrm{Perimeter}(△DEF)}=\frac{AB}{DE} \\ \Rightarrow \frac{\mathrm{Perimeter}(△ABC)}{25}=\frac{9.1}{6.5} \\ \Rightarrow \mathrm{P}\mathrm{erimeter}(△ABC)=\frac{9.1\times 25}{6.5}=35\mathrm{cm} \end{gathered}$$