Question

∆ABC ∼ ∆DEF and their perimeters are 32 cm and 24 cm respectively. If AB = 10 cm, then DE =?
(a) 8 cm
(b) 7.5 cm
(c) 15 cm
(d) $5\sqrt{3}\mathrm{cm}$

Answer 1

(b) 7.5 cm

$\because$ ∆ABC ∼ ∆DEF

$$\begin{gathered} \therefore \frac{\mathrm{Perimeter}(△\mathrm{ABC})}{\mathrm{Perimeter}(△\mathrm{DEF})}=\frac{\mathrm{AB}}{\mathrm{DE}} \\ \Rightarrow \frac{32}{24}=\frac{10}{DE} \end{gathered}$$

$\Rightarrow DE=\frac{10\times 24}{32}=7.5\mathrm{cm}$