Question

If the area of an equilateral triangle is$20\sqrt{3}c{m}^2,$ then its perimeter is

• A.
  $12\sqrt{5}cm$
• B.
  $6\sqrt{5}cm$
• C.
  $8\sqrt{5}cm$
• D.
  $4\sqrt{5}cm$

Answer 1

The correct option is A

$12\sqrt{5}cm$
Let the side of an equilateral triangle be a.

Also, the area of the equilateral triangle is $20\sqrt{3}c{m}^2.\Rightarrow \frac{\sqrt{3}}{4}\times a^2=20\sqrt{3}\Rightarrow a^2=20\times 4\Rightarrow a^2=4\times 5\times 4\Rightarrow a=4\sqrt{5}cm\therefore \text{Perimeter of the equilateral triangle}=3\times a=3\times 4\sqrt{5}=12\sqrt{5}cm$

Hence, the correct answer is option (a).