Question

D, E, F are midpoints of sides BC, CA and AB of $△ABC$. If the perimeter of $△ABC$ is $12.8$cm, then the perimeter of $△DEF$ is :

• A. $17cm$
• B. $38.4cm$
• C. $25.6cm$
• D. $6.4cm$

Answer 1

The correct option is D $6.4cm$

Given perimeter of $△ABC=12.8cm$

$\Rightarrow AB+BC+AC=12.8cm$

$DE=\frac{1}{2}AB,EF=\frac{1}{2}BC$ and $DF=\frac{1}{2}AC$

$\therefore AB=2DE,BC=2EF,AC=2DF$

As, $D,E,F$ are the mid points of $BC,AB$ and $AC$

$\therefore$ By mid point theorem, the equations are possible

$\Rightarrow 2DE+2EF+2DF=12.8cm$

$\Rightarrow DE+EF+DF=\frac{12.8}{2}=6.4cm$

i.e, perimeter of $△DEF=DE+EF+DF=6.4cm$