Question

Sabendo R e S transversais de um faixe de paralelas, cálcule X e Y ​

Answer 1

Utilizando o Teorema de Tales, podemos montar a seguinte relação:

$\boxed{\frac{x}{4}~=~\frac{y}{10}}\\\\\\Como~temos~1~equacao~e~2~incognitas,~precisaremos~de~outra\\equacao~para~poder~resolver.\\\\\\Pelo~desenho~temos~que:~\boxed{x+y~=~21}\\\\\\Isolando~o~"x"~e~substituindo~na~relacao~achada~anteriormente:\\\\\\\frac{21-y}{4}~=~\frac{y}{10}\\\\\\Multiplicando~Cruzado\\\\\\4~.~y~=~10~.~(21-y)\\\\\\4y~=~210-10y\\\\\\4y+10y~=~210\\\\\\y~=~\frac{210}{14}\\\\\\\boxed{y~=~15}\\\\\\Vamos,~por~fim,~achar~o~valor~de~"x":\\\\\\x+y~=~21$

$x+15~=~21\\\\\\x~=~21-15\\\\\\\boxed{x~=~6}$