Question

In an equilateral △ABC, D, E and F are the midpoints of sides BC, CA and AB respectively. The perimeter of △ABC is times the perimeter of △DEF.

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

The correct option is A 2

Let the side of △ABC be 'x' cm.
Perimeter of △ABC = 3x cm
In △ABC,F and E are the mid-points of AB and AC,
By midpoint theorem,
$\therefore EF=\frac{1}{2}BC=\frac{1}{2}\times x=\frac{x}{2}cm$
$⟹$The side of △DEF $=\frac{x}{2}cm$,
$\therefore$ Perimeter of △DEF = 3 $\times$ side of △DEF
$=3\times \frac{x}{2}=\frac{3x}{2}cm$
Hence, the perimeter of △ABC is 2 times the perimeter of △DEF.