what is the radius of the circumscribed circle for the triangle in which a=13, b= 21, and c=29?

Answer 1

First apply Heron's formula:
s = (a + b + c)/2 = 63/2 = 31.5
The area of the triangle is:
sqrt{s(s-a)(s-b)(s-c)} = sqrt(31.5*2.5*10.5*18.5)
= (1/4)sqrt(63*5*21*37)
= (21/4)sqrt(15*37)
Another way to calculate the area is:
abc/4R
Hence the radius of the circumscribed circle is:
R = 13*21*29/[4*(21/4)sqrt(15*37)]
= 13*29 / sqrt(15*37)
= 377/ sqrt(555)
= 377*sqrt(555)/555