The radius of the incircle of the equilateral triangle having each side 6 cm is

June 28, 2016 Quiz Questions

The radius of the incircle of the equilateral triangle having each side 6 cm is
[A]3cm
[B]\sqrt{3}cm
[C]2\sqrt{3}cm
[D]6\sqrt{3}cm

\mathbf{\sqrt{3}cm}
E = In-center, AD ⊥ BC
AB = 6 cm, BD = 3 cm
∠ADB = 90°
∴ AD = \sqrt{AB^{2} - BD^{2}}
=> \sqrt{6^{2}-3^{2}} = \sqrt{36-9}
=> \sqrt{27} = 3\sqrt{3}cm
∴ In-radius = \frac{1}{3}AD
=>\frac{1}{3}\times 3\sqrt{3} = \sqrt{3}cm
Hence option [B] is the right answer.

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