Question 68

Radius of the in-circle of an equilateral ΔABC of sides $$2\sqrt3$$ units is x cm. The value of x is

Solution

In-radius of a triangle = $$r=\frac{\triangle}{s}$$

Side of equilateral triangle = $$2\sqrt3$$ units

=> Semi-perimeter = $$s=\frac{2\sqrt3+2\sqrt3+2\sqrt3}{2}=3\sqrt3$$ units

Area of triangle = $$\triangle =\frac{\sqrt3}{4}a^2$$

= $$\frac{\sqrt3}{4} \times (2\sqrt3)^2=3\sqrt3$$

$$\therefore$$ $$r=\frac{3\sqrt3}{3\sqrt3}=1$$

=> Ans - (C)

Share on Whatsapp Share on Whatsapp

Create a FREE account and get: