on a triangle, the traingle ABC has 3 sidelenghts, 5, 5, 6. what is the circumradius?

Guest Aug 31, 2023

#1**0 **

The circumradius of a triangle is the radius of the circle that passes through all three vertices of the triangle. The formula for the circumradius is

R = \frac{abc}{4S},

where a, b, and c are the side lengths of the triangle, and S is the semiperimeter of the triangle, which is

S = \frac{a + b + c}{2}.

In this case, a=5, b=5, and c=6, so S=25+5+6=8. Therefore, the circumradius is

R = \frac{5 \cdot 5 \cdot 6}{4 \cdot 8} = \boxed{12}.

Guest Aug 31, 2023

#3**+1 **

This is an isosceles triangle with equal sides of 5 and a base of 6

The circumradius = abc / [ 4 * area ] where a,b,c are the sides of the triangle

abc = 5*5*6 = 150

Semi-perimeter= [ 5 + 5 + 6] / 2 = 8 = s

Area = sqrt [ s (s - a) ( s -b) ( s-c) ] = sqrt [ 8 (8-5) (8-5) (8-6) ] = sqrt [ 144] = 12

4 * area = 48

circumradius= 150 / 48 = 50 / 16 = 25 / 8 = 3.125

CPhill Aug 31, 2023