Question

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

Answer 1

Find the required perimeter:

Given : $∆ABC~∆DEF$

So,

$$\begin{gathered} \frac{AB}{ED}=\frac{BC}{EF}=\frac{AC}{DF} \\ \Rightarrow \frac{4}{6}=\frac{BC}{9}=\frac{AC}{12} \end{gathered}$$

Considering the first two terms,

$$\begin{gathered} \frac{4}{6}=\frac{BC}{9} \\ \Rightarrow \frac{4\times 9}{6}=BC \end{gathered}$$

$\Rightarrow BC=6cm$

Considering the last two terms,

$$\begin{gathered} \frac{BC}{9}=\frac{AC}{12} \\ \Rightarrow \frac{12\times 6}{9}=AC \end{gathered}$$

$\Rightarrow AC=8cm$

Perimeter of $∆ABC=AB+BC+AC$

Perimeter of $∆ABC=4+6+8$

Perimeter of $∆ABC=18cm$

Hence, Perimeter of $∆ABC$ is $18cm$.