If area of a circle inscribed in an equilateral triangle is 48$\pi$ square units, then perimeter of the triangle is

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KollegeApply · Accepted Answer

Let the circle of radius r be inscribed in an equilateral triangle of side a. Area of the circle is given as 48$\pi$. $\Rightarrow$ pir^2=48pi $\Rightarrow$ r^2=48 $\Rightarrow$ r=4sqrt3 Now, it is clear that ON⊥BC. So, ON is the height of ΔOBC corresponding to BC. Area of ΔABC = Area of ΔOBC + Area of ΔOCA + Area of ΔOAB = 3 $\times$ Area of ΔOBC sqrt3/4xxa^2=3xx1/2xxBCxxON sqrt3/4xxa^2=3xx1/2xxaxxr `sqrt3/4xxa^2=3xx1/2xxaxx4sqrt3 a=24` Thus, perimeter of the equilateral triangle = 3 $\times$ 24 units = 72 units [Solution diagram: 64096_solution_1.png]

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