Question

Considere a figura abaixo, em que as retas r, s e t são paralelas entre si. A soma a + b + c é igual a: 9, 10, 12, 16 ou 18?

Answer 1

Olá Sofia,


Podemos resolver essa tarefa aplicando o teorema de Tales:


$\mathsf{\dfrac{2}{4}=\dfrac{a}{3}\Rightarrow 4a=6\Rightarrow a=\dfrac{\diagup\!\!\!\!6}{\diagup\!\!\!\!4}\Rightarrow a=\dfrac{3}{2}}\\\\\\\\\mathsf{\dfrac{\dfrac{3}{2}}{3}=\dfrac{4}{b}\Rightarrow \dfrac{3b}{2}=12\Rightarrow b=\dfrac{12\cdot 2}{3}\Rightarrow b=8}\\\\\\\\\mathsf{\dfrac{4}{8}=\dfrac{c}{5}\Rightarrow 8c=20\Rightarrow c=\dfrac{\diagup\!\!\!\!20}{\diagup\!\!\!\!8}\Rightarrow c = \dfrac{5}{2}}$

$\mathsf{a+b+c\Rightarrow \dfrac{3}{2}+8+\dfrac{5}{2}\Rightarrow \dfrac{3+5+16}{2}\Rightarrow \dfrac{24}{2}=\boxed{\mathsf{12}}}$

Dúvidas? comente

Answer 2

A soma a + b + c = 12

a = 3

b = 4

c = 5

Somando 3 + 4 + 5 = 12