Question

If the area of an equilateral triangle is $25\sqrt{3}c{m}^2$, then its perimeter = ____ cm.

• A. 10
• B. 30
• C. 45
• D. 60

Answer 1

The correct option is B

30

Area of an equilateral triangle with side 'a' is given by $\frac{\sqrt{3}}{4}{a}^2$.
Given, area = $25\sqrt{3}{\text{cm}}^2$

$⟹25\sqrt{3}=\frac{\sqrt{3}}{4}{a}^2$

$⟹a^2=5^2\times 2^2$

$\therefore a=10\text{cm}$

Then, Perimeter =$3a$

= $3\left(10\right)$

= $30\text{cm}$