Question

(50 PONTOS) Um pino tem a forma triangular de medidas 4mm, 5mm e 6mm. Ele deve ser encaixado exatamente num furo circular. Calcule o diâmetro desse furo. (Quero o cálculo).

Answer 1

a ⋅ b ⋅ c 
R =
  √ [ (a + b + c) ⋅ (−a + b + c) ⋅ (a − b + c) ⋅ (a + b − c) ] 

Onde.
R: circunraio 
a, b e c: medidas dos lados do triângulo. 

        4 ⋅ 5 ⋅ 6 
R =
  √ [ (4 + 5 + 6) ⋅ (−4 + 5 + 6) ⋅ (4 − 5 + 6) ⋅ (4 + 5 − 6) ] 

        120 
R =
  √ [ ( 15 ) ⋅ ( 7 ) ⋅ ( 5 ) ⋅ ( 3 ) ] 

       120 
R =  
  √ [ ( 15 ) ⋅ ( 7 ) ⋅ ( 15 ) ] 

     120 
R =
  √ [ ( 15 )² ⋅ ( 7 ) ] 

   120 
R =
  15 ⋅ √ ( 7 ) 

   8 
R = mm 
   √ ( 7 )