Question

If $\Delta ABC\sim \Delta DEF$, AB = 4cm, DE = 6, EF = 9cm and FD = 12cm, then find the perimeter of $\Delta ABC$.

Answer 1

Given, AB = 4cm, DE = 6cm, and EF 9cm and FD = 12cm
Also $\Delta ABC\sim \Delta DEF$
$\therefore$ $\frac{AB}{ED}=\frac{BC}{EF}=\frac{AC}{DF}$
$\Rightarrow \frac{4}{6}=\frac{BC}{9}=\frac{AC}{12}$
On taking first two terms, we get
$\frac{4}{6}=\frac{BC}{9}$
$\Rightarrow BC=\frac{4\times 9}{6}=6cm$
$=AC=\frac{6\times 12}{9}=8cm$
Now, perimeter of $\Delta ABC=AB+BC+AC$
$=4+6+8=18cm$