Question

Na figura, determine as medida x e y, sabendo que r//s//t e AC=27

Answer 1

Como as retas "r", "s" e "t" são paralelas, podemos utilizar o teorema de Tales para achar relações entres as medidas:

$\boxed{\dfrac{AB}{DE}~=~\dfrac{AC}{DF}}\\\\\\Substituindo~os~valores:\\\\\\\dfrac{x}{5}~=~\dfrac{27}{5+4}\\\\\\\dfrac{x}{5}~=~\dfrac{27}{9}\\\\\\Multiplicando~cruzado:\\\\\\9~.~x~=~5~.~27\\\\\\x~=~\dfrac{5~.~27}{9}\\\\\\\boxed{x~=~15~cm}$

$\boxed{\dfrac{BC}{EF}~=~\dfrac{AC}{DF}}\\\\\\Substituindo~os~valores:\\\\\\\dfrac{y}{4}~=~\dfrac{27}{9}\\\\\\Multiplicando~cruzado:\\\\\\9~.~y~=~4~.~27\\\\\\y~=~\dfrac{4~.~27}{9}\\\\\\\boxed{y~=~12~cm}$