Question

The perimeter of an equilateral triangle is $60m.$ The area is

• A. $15\sqrt{3}{m}^2$
• B. $10\sqrt{3}{m}^2$
• C. $20\sqrt{3}{m}^2$
• D. $100\sqrt{3}{m}^2$

Answer 1

The correct option is D $100\sqrt{3}{m}^2$

Given: Perimeter of an equilateral triangle $=60m$

Leteach side of an equilateral triangle be $x$

$\therefore x+x+x=60$

$\Rightarrow 3x=60$

$\Rightarrow x=\frac{60}{3}=20m$

$\therefore$ Area of an equilateral triangle $=\frac{\sqrt{3}}{4}(side{)}^2$

$=\frac{\sqrt{3}}{4}\times 20\times 20$

$=100\sqrt{3}{m}^2$

Hence, $\left(d\right)$ is the correct answer.