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