Question

The side of an equilateral triangle is $20\sqrt{3}cm$. The numerical value of the radius of the circle circumscribing the triangle is:

• A. $20cm$
• B. $20\sqrt{3}cm$
• C. $20\pi cm$
• D. $\frac{20}{\pi }$

Answer 1

The correct option is A $20cm$

Let

$\text{r=inradius of circle, R=circumradius, A=area of triangle, S=semi-perimeter of triangle}$

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

$=>\frac{\sqrt{3}}{4}\times (20\sqrt{3}{)}^2$

$=>300\sqrt{3}$

Now,

$S=\frac{20\sqrt{3}+20\sqrt{3}+20\sqrt{3}}{2}$

$=>S=30\sqrt{3}$

Now,

$r=A/S$

$=>\frac{300\sqrt{3}}{30\sqrt{3}}$

$=>10$

According to formulae,

$R=2r$

$=>R=20$cm.