Question

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

(a) 17$\sqrt{3}$ units

(b) 36 units

(c) 72 units

(d) 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.

⇒ πr² = 48π

⇒ r² = 48

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

Thus, perimeter of the equilateral triangle = 3 × 24 units = 72 units

So the answer is (c).