Question

Question 7
$If\Delta ABC\sim \Delta DEF$,
AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, then find the perimeter of $\Delta ABC$.

Answer 1

Given, AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm
$Also\Delta ABC\sim \Delta DEF$

$\therefore \frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}$

$\Rightarrow \frac{4}{6}=\frac{BC}{9}=\frac{AC}{12}...\left(i\right)$

On taking first two terms, we get,
$\frac{4}{6}=\frac{BC}{9}$
$\Rightarrow BC=\frac{4\times 9}{6}=6cm$
$=AC=\frac{6\times 12}{9}=8cm$ (taking last two term of eq(i))
Now, perimeter of $\Delta ABC=AB+BC+AC$
$=4+6+8=18cm$