Question

Considere os pontos A(0,0), B(3,4) e C(15,8). a) Calcule o perímetro do triangulo ABC

Answer 1

Calcule as distâncias entre os pontos: AB ;  BC e AC, então irá encontrar a medida de cada lado, e poderá calcular o perímetro:

$\Large\boxed{Fo\´rmula\to~~D_{A,B}= \sqrt{(x_b-x_a)^2+(y_b-y_a)^2} }$


$A~(0,0),~~ B~(3,4) ~~e~~ C~(15,8)$




$D_{A,B}= \sqrt{(3-0)^2+(4-0)^2} \to ~~D_{A,B}= \sqrt{(3)^2+(4)^2} \to \\\\D_{A,B}= \sqrt{9+16} \to ~~ D_{A,B}= \sqrt{25} \to ~~\large\boxed{\boxed{ D_{A,B}=5}}$



$D_{B,C}= \sqrt{(15-3)^2+(8-4)^2} \to ~~D_{B,C}= \sqrt{(12)^2+(4)^2} \to \\\\D_{B,C}= \sqrt{144+16} \to ~~ D_{B,C}= \sqrt{160} \to ~~D_{B,C}= \sqrt{2^2.2^2.2.5} \to \\\\ D_{B,C}= 2.2\sqrt{2.5} \to~~ \large\boxed{\boxed{ D_{B,C}=4 \sqrt{10} }}$




$D_{A,C}= \sqrt{(15-0)^2+(8-0)^2} \to ~~D_{A,C}= \sqrt{(15)^2+(8)^2} \to \\\\D_{A,C}= \sqrt{225+64} \to ~~ D_{A,C}= \sqrt{289} \to ~~\large\boxed{\boxed{ D_{A,C}=17}}$



Achamos:

AB = 5
BC = 4√10
AC = 17


Perímetro = Soma de todos os lados, logo:

P = AB + BC + AC ---> 
P = 5 + 4√10 + 17 --->
P = 22 + 4√10  ou 
P ≈ 34,65