Question

Me ajudem por favor a calcular o valor do x e y

Answer 1

Como os segmentos AB e DE são paralelos, podemos afirmar que os triângulos ABC e CDE são semelhantes.

Sendo assim, podemos montar uma relação entre suas medidas.

$\boxed{\frac{AB}{DE}~=~\frac{AC}{DC}~=~\frac{BC}{EC}}\\\\\\Vamos~comecar~determinando~"x":\\\\\\\frac{AC}{DC}~=~\frac{BC}{EC}\\\\\\\frac{25}{x}~=~\frac{12+8}{8}\\\\\\Multiplicando~Cruzado\\\\\\x~.~(12+8)~=~25~.~8\\\\\\20x~=~200\\\\\\x~=~\frac{200}{20}\\\\\\\boxed{x~=~10}\\\\\\\\Agora,~determinando~"y":\\\\\\\frac{AB}{DE}~=~\frac{BC}{EC}\\\\\\\frac{15}{y}~=~\frac{12+8}{8}\\\\\\Multiplicando~Cruzado\\\\\\y~.~(12+8)~=~15~.~8\\\\\\20y~=~120$

$y~=~\frac{120}{20}\\\\\\\boxed{y~=~6}$