A 07.10, alguém pode me ajudar achar a medida do raio da circunferência. Vai dar E.
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Boa tarde Fernada!
Solução!
Vamos usar a formula de Herão para determinarmos o raio da circunferência.
Semi perímetro do triangulo.
![S~~perimetro= \dfrac{a+b+c}{2}\\\\\
S~~perimetro= \dfrac{7+8+9}{2}\\\\\
S~~perimetro= \dfrac{24}{2}\\\\\
S~~perimetro=12\\\\\
Calculo da area do triangulo.\\\\\\\\\
(Area)^{2}=p(p-l1).(p-l2).(p-l3)\\\\\\
(Area)^{2}=12(12-7).(12-8).(12-9)\\\\\\
(Area)^{2}=12(5).(4).(3)\\\\\\
(Area)^{2}=12(60)\\\\\\
(Area)^{2}=720\\\\\\
(Area)}= \sqrt{720} \\\\\\
Area=12 \sqrt{5}](https://tex.z-dn.net/?f=S%7E%7Eperimetro%3D+%5Cdfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5C%5C%5C%5C%5C+%0AS%7E%7Eperimetro%3D+%5Cdfrac%7B7%2B8%2B9%7D%7B2%7D%5C%5C%5C%5C%5C+%0AS%7E%7Eperimetro%3D+%5Cdfrac%7B24%7D%7B2%7D%5C%5C%5C%5C%5C+%0AS%7E%7Eperimetro%3D12%5C%5C%5C%5C%5C%0A%0ACalculo+da+area+do+triangulo.%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%0A%28Area%29%5E%7B2%7D%3Dp%28p-l1%29.%28p-l2%29.%28p-l3%29%5C%5C%5C%5C%5C%5C%0A%28Area%29%5E%7B2%7D%3D12%2812-7%29.%2812-8%29.%2812-9%29%5C%5C%5C%5C%5C%5C+%0A%28Area%29%5E%7B2%7D%3D12%285%29.%284%29.%283%29%5C%5C%5C%5C%5C%5C+%0A%28Area%29%5E%7B2%7D%3D12%2860%29%5C%5C%5C%5C%5C%5C+%0A%28Area%29%5E%7B2%7D%3D720%5C%5C%5C%5C%5C%5C+%0A%28Area%29%7D%3D+%5Csqrt%7B720%7D+%5C%5C%5C%5C%5C%5C+%0AArea%3D12+%5Csqrt%7B5%7D+%0A "S~~perimetro= \dfrac{a+b+c}{2}\\\\\
S~~perimetro= \dfrac{7+8+9}{2}\\\\\
S~~perimetro= \dfrac{24}{2}\\\\\
S~~perimetro=12\\\\\
Calculo da area do triangulo.\\\\\\\\\
(Area)^{2}=p(p-l1).(p-l2).(p-l3)\\\\\\
(Area)^{2}=12(12-7).(12-8).(12-9)\\\\\\
(Area)^{2}=12(5).(4).(3)\\\\\\
(Area)^{2}=12(60)\\\\\\
(Area)^{2}=720\\\\\\
(Area)}= \sqrt{720} \\\\\\
Area=12 \sqrt{5}")
Calculo do perímetro do triangulo
Calculo do raio da circunferência inscrita.
![r= \dfrac{2Area}{Perimetro}\\\\\\\\\
r= \dfrac{2(12 \sqrt{5} )}{24}\\\\\\\\
r= \dfrac{24 \sqrt{5} }{24}\\\\\\\\
r= \sqrt{5}](https://tex.z-dn.net/?f=r%3D+%5Cdfrac%7B2Area%7D%7BPerimetro%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A+r%3D+%5Cdfrac%7B2%2812+%5Csqrt%7B5%7D+%29%7D%7B24%7D%5C%5C%5C%5C%5C%5C%5C%5C%0Ar%3D+%5Cdfrac%7B24+%5Csqrt%7B5%7D+%7D%7B24%7D%5C%5C%5C%5C%5C%5C%5C%5C%0Ar%3D+%5Csqrt%7B5%7D+ "r= \dfrac{2Area}{Perimetro}\\\\\\\\\
r= \dfrac{2(12 \sqrt{5} )}{24}\\\\\\\\
r= \dfrac{24 \sqrt{5} }{24}\\\\\\\\
r= \sqrt{5}")
Boa tarde!
Bons estudos!
Solução!
Vamos usar a formula de Herão para determinarmos o raio da circunferência.
Semi perímetro do triangulo.
Calculo do perímetro do triangulo
Calculo do raio da circunferência inscrita.
Boa tarde!
Bons estudos!
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