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

 Aug 31, 2023
 #1
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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}.

 Aug 31, 2023
 #2
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hey, what does the answer say and the explination? it shows as some really weird symbols.

Guest Aug 31, 2023
 #3
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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  

 

cool cool cool

 Aug 31, 2023

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