Question

Consider an equilateral triangle in which the
length of one side is 6 cm. Find the radius of the
incircle of the triangle.
​

Answer 1

Answer:

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.