Question

Given $△$ DEF $\sim$ $△$ABC. If AB = 4 cm, BC = 2 cm, CA = 3 cm and EF = 4 cm, then the perimeter of $△$DEF is ____ cm.

• A. 18
• B. 15
• C. 16
• D. 14

Answer 1

The correct option is A

18

Given $△$ DEF $\sim$ $△$ABC.

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

$\frac{4}{DE}=\frac{3}{DF}=\frac{2}{4}=\frac{1}{2}$

$\frac{Perimeter\left(△ABC\right)}{Perimeter\left(△DEF\right)}=\frac{1}{2}$

$\frac{9}{Perimeter\left(△DEF\right)}=\frac{1}{2}$ .......(ratio of perimeters of similar triangles)

$Perimeter\left(△DEF\right)$ = 18 cm