The area of a circle inscribed in an equilateral triangle is 346.5 cm^2. Find the perimeter of the triangle. (Use Pi = 22/7 and Sqrt3 = 1.73).
OPtion
1) 102.45 cm
2) 104.33 cm
3) 89.54 cm
4) 108.99 cm
5) 94.35 cm
6) 72.66 cm
7) 112.33 cm
8) 110.5 cm
9) 86.5 cm
10)None of these
Solution
By using figure
The incentre of the triangle is coincident with centroid (as it is an equilateral triangle)
Also I divided AD in the ratio 2:1 (I is centroid)
We have, area of circle = 346.5 cm^2
=> Pi r^2 = 346.5
r^2 = 346.5*7/22 = 110.25
r = 10.5
In triangle ABC
We have ID = AI = 1:2
ID = r = 1/3 AD
Also as triangle ABC is equilateral
AD = (Sqrt3/2)*a (From pythagoras theorem is Triangle ADB)
r = Sqrt3*a/2 * 1/3 = a/2*Sqrt3
a = 2*Sqrt3*r
Perimeter = 3a
= 3*2*Sqrt3*r = 108.99 cm.