Question

$\Delta DEF~\Delta ABC$.
If DE = 6 cm, EF = 10 cm, FD = 5 cm, and AB = 4 cm, find the perimeter of $\Delta ABC$.

[1 mark]

• A. 42 cm
• B. 28 cm
• C. 21 cm
• D. 14 cm

Answer 1

The correct option is D 14 cm

Given,
$\Delta DEF\sim \Delta ABC$
$\therefore \frac{DE}{AB}=\frac{EF}{BC}=\frac{FD}{CA}=\frac{Perimeterof\Delta DEF}{Perimeterof\Delta ABC}$

$\text{Perimeter of}\Delta DEF=DE+EF+FD=6+10+5=21cm$

$\therefore \frac{6}{4}=\frac{21}{Perimeterof\Delta ABC}$
$\Rightarrow Perimeterof\Delta ABC=14cm$