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) $5 \sqrt{3} \mathrm{~cm}$
Solution:
(b) 7.5 cm
$\because \Delta A B C \sim \triangle D E F$
$\therefore \frac{\text { Perimeter }(\triangle \mathrm{ABC})}{\text { Perimeter }(\triangle \mathrm{DEF})}=\frac{\mathrm{AB}}{\mathrm{DE}}$
$\Rightarrow \frac{32}{24}=\frac{10}{D E}$
$\Rightarrow D E=\frac{10 \times 24}{32}=7.5 \mathrm{~cm}$
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