The radius of the incircle of the equilateral triangle having each side 6 cm is
The radius of the incircle of the equilateral triangle having each side 6 cm is
[A]$latex 3cm$
[B]$latex \sqrt{3}cm$
[C]$latex 2\sqrt{3}cm$
[D]$latex 6\sqrt{3}cm$
$latex \mathbf{\sqrt{3}cm}$
E = In-center, AD ⊥ BC
AB = 6 cm, BD = 3 cm
∠ADB = 90°
∴ AD = $latex \sqrt{AB^{2} – BD^{2}}$
$latex => \sqrt{6^{2}-3^{2}} = \sqrt{36-9}$
$latex => \sqrt{27} = 3\sqrt{3}cm$
∴ In-radius = $latex \frac{1}{3}&s=1$$latex AD$
$latex =>\frac{1}{3}\times 3\sqrt{3}&s=1$ $Latex = \sqrt{3}cm$
Hence option [B] is the right answer.