Multiple choice

The area of circle inscribed in an equilateral triangle is 48 square units Then the perimeter of the triangle is ( in units)

  1. $ \displaystyle 72\sqrt{3} $
  2. $ \displaystyle 48\sqrt{3} $

  3. 72

  4. 36
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C Correct answer
AI explanation

Using the area formula for a circle, the inradius squared equals 48 divided by pi, which simplifies the inradius to 4 times the square root of 3. For an equilateral triangle, the height is 3 times the inradius, yielding a height of 12 times the square root of 3. Because the height of an equilateral triangle is (root 3 divided by 2) times its side, the side length is 24, resulting in a perimeter of 72 units.

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