Question : The radius of the incircle of the equilateral triangle having each side 6 cm is:
Option 1: $2 \sqrt 3$
Option 2: $\sqrt 3$
Option 3: $6 \sqrt 3$
Option 4: $2$
Correct Answer: $\sqrt 3$
Solution :
For an equilateral triangle, the radius of the incircle is given by:
$r=\frac{a}{2\sqrt3}$, where $a$ is the side of the equilateral triangle
Side of an equilateral triangle = 6 cm
$\therefore$ The radius of the incircle, $r=\frac{a}{2\sqrt3}$
Putting the values, we get:
$r=\frac{6}{2\sqrt3} = \sqrt3$
Hence, the correct answer is $\sqrt3$.
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