Question

O segmento AC mede 22,5cm sabendo que r//s//t, calcule "x" e "y":​

Answer 1

Utilizando o teorema de Tales, temos:

$\frac{x}{y}~=~\frac{5}{4}\\\\\\\frac{x}{AC-x}~=~\frac{5}{4}\\\\\\4~.~x~=~(22,5-x)~.~5\\\\\\4x~=~112,5-5x\\\\\\9x~=~112,5\\\\\\x~=~\frac{112,5}{9}\\\\\\\boxed{x~=~12,5\,cm}$

Calculando "y":

$AC ~=~ x + y\\\\\\22,5~=~12,5+y\\\\\\y~=~22,5-12,5\\\\\\\boxed{y~=~10\,cm}$