SOLUTION: An equilateral triangle with a perimeter of 24 square root (3) is inscribed in circle . find radius of the circle

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Question 351554: An equilateral triangle with a perimeter of 24 square root (3) is inscribed in circle . find radius of the circle
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Hi,
Using Heron's formula will give us the Area:
Note: the sides a, b, c are each = 8%2Asqrt%283%29 and the semi-perimeter = 12%2Asqrt%283%29
.
applying Heron's formula
A=+sqrt%28+12%2Asqrt%283%29%2A4%2Asqrt%283%29%2A4%2Asqrt%283%29%2A4%2Asqrt%283%29%29
A=+sqrt%28+12%2A+9%2A64%29
A=+2%2A3%2A8+%2Asqrt%28+3%29=+48+%2Asqrt%283%29
.
The radius of the circumscribed circle is:

simplify and solve for R