Question:
If ΔABC ~ ΔDEF, AB = 4 cm, DE = 6, EF = 9 cm and FD = 12 cm, then find the perimeter of Δ ABC.
Solution:
Given AB = 4cm, DE = 6cm and EF = 9cm and FD = 12 cm
Also, $\triangle A B C \sim \triangle D E F$
$\therefore$ $\frac{A B}{E D}=\frac{B C}{E F}=\frac{A C}{D F}$
$\Rightarrow$ $\frac{4}{6}=\frac{B C}{9}=\frac{A C}{12}$
On taking first two terms, we get
$\frac{4}{6}=\frac{B C}{9}$
$\Rightarrow$ $B C=\frac{4 \times 9}{6}=6 \mathrm{~cm}$
$=A C=\frac{6 \times 12}{9}=8 \mathrm{~cm}$
Now, $\quad$ perimeter of $\triangle A B C=A B+B C+A C$
$=4+6+8=18 \mathrm{~cm}$
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