Question

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

विकल्प

•  17 \[\sqrt{3}\]units 

• 36 units

• 72 units

• 48\[\sqrt{3}\]units

Answer 1

Let the circle of radius r be inscribed in an equilateral triangle of side a.

Area of the circle is given as 48π. 

`⇒ pir^2=48pi`

`⇒ r^2=48`

`⇒ 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 × 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 × 24 units = 72 units