Question

calcule o perimetro do triangulo A (8,3) B (4 7) c(2 1)

Answer 1

Para o perímetro basta somar a distância ... 

P = AB + AC + BC        ( teorema de Pitágoras ) 


$P=\sqrt{(4-8)^{2}+(7-3) ^{2} } + \sqrt{(2-8)^{2} +(1-3)^{2} } + \sqrt{(2-4)^{2}+(1-7)^{2} }$


$P= \sqrt{(-4)^{2}+(4)^{2} } + \sqrt{(-6)^{2}+(-2)^{2} } + \sqrt{(-2)^{2}+(-6)^{2}}$


$P= \sqrt{16+16} + \sqrt{36+4} + \sqrt{4+36}$


$P= \sqrt{32} + \sqrt{40} + \sqrt{40}$


$P= \sqrt{4^{2}.2} + \sqrt{2^{2}.10} + \sqrt{2^{2}.10}$


$P=4 \sqrt{2} +2 \sqrt{10} +2 \sqrt{10}$


$\boxed{\boxed{P=4 \sqrt{2} +4 \sqrt{10} }}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ok$