Question

If the length of each median of an equilateral triangle is 4 cm then the perimeter of the triangle is

• A. $7\sqrt{3}$ cm
• B. $8\sqrt{3}$ cm
• C. $9\sqrt{3}$ cm
• D. $10\sqrt{3}$ cm

Answer 1

The correct option is B $8\sqrt{3}$ cm

Given length of each mediuan equilateral triangle is 4 cm

We know that medians m of equilateral triangle=$\frac{\sqrt{3}}{2}a$ (where a is the length of sides)

$\therefore 4=\frac{\sqrt{3}}{2}a\Rightarrow a=\frac{8}{\sqrt{3}}$ cm

Than perimeter of equilateral triangle =$3\times \frac{8}{\sqrt{3}}=8\sqrt{3}$ cm