The area of circle inscribed in an equilateral triangle is 154 sq cm. What is the perimeter of the triangle?

• A. 21 cm
• B. 42 cm
• C. 21?3 cm
• D. 42?3 cm

Answer: (D)

We know that, the radius of a circle inscribed in a equilateral triangle = a/[2?3]Where, a be the length of the side of an equilateral triangle.Given that, area of a circle inscribed in an equilateral tringle = 154 cm2? ?(a/2?3)2 = 154? (a/2?3)2 = 154 x (7/22) = (7)a2? a = 42?3 cmPerimeter of an equilateral triangle = 3a = 3(14?3) = 42?3 cm