Answer: The radius = 5 cm
Step-by-step explanation:
You can use the formula r = area/semi-perimeter.
The semi perimeter (s) = (10√3 + 10√3 + 10√3)/2 = 15√3
The area of the triangle can be found √s(s-a)(s-b)(s-c) where a b c are the sides of the triangle.
As all sides are equal, s-a = s-b = s-c then, √s(s-a)(s-b)(s-c) = √s(s-a)²×(s-a)
(s-a)√s(s-a). now substituting values, s-a = 15√3-10√3 = 5√3
(s-a)√s(s-a) = (5√3)√15√3 × 5√3 = 5√3 × 15 = 75√3
Therefore, area of triangle = 75√3
r = 75√3/15√3 = 5.