The radius of the incircle of an equilateral DABC of side 2√3 units is x cm. The value of x is

The correct option is 1.

Let the equilateral triangle be denoted as ΔABC. We are given that the side length of this equilateral triangle, which we can denote as a, is equal to 2√3 units.
That is:

$a=2\sqrt{3}$

For any equilateral triangle of side length a, the radius of the incircle (also known as the inradius, denoted as r) is related to the side length by the standard formula:

$r=\frac{a}{2\sqrt{3}}$

To find the value of the inradius x (where x = r), we substitute the given value of the side length a into the formula:

$x=\frac{2\sqrt{3}}{2\sqrt{3}}$

Simplifying the fraction by canceling the common term 2√3 from both the numerator and the denominator, we get:

$x=1$

Therefore, the radius of the incircle is 1 unit (or 1 cm as defined in the question), which corresponds to the option with the value 1.