Question

The area of circle inscribed in an equilateral triangle is 48 sq. units. the perimeter of triangle is ?

Answer 1

Solution:-
Given : The area of the circle = 48 sq units.
Let the radius of circle be r.
⇒ area of a circle = πr²
48 = 22/7r²
r² = (48×7)/22
r² = 15.272727
r = √15.272727
r = 3.91 units
As the center of circle is the point of intersection of the angular bisector.
Suppose ABC be the equilateral triangle and AD = h be the altitude.
Hence the bisectors are also the altitudes and medians, whose point of intersection divides the median in the ratio 2 : 1.
∠ ADB = 90° and OD = (1/3)AD
so, r = (h/3)
h = 3r
Or, h = 3×3.91
h = 11.73 units.
Let the each side of the equilateral triangle be 'a' then altitude of an equilateral triangle is (√3/2) times its side.
That is h = (√3a/2)
⇒ a = 2h/√3

= (2 × 11.73)/√3
= 23.46/√3
= 23.46/1.73
a = 13.56 units
Perimeter of the equilateral triangle = 3a
= 3 × 13.56
Perimeter = 40.68 units
Answer.