Question

Calcule x e y. sabendo que AB//DE; AB= 1,5 cm; AC= 2,5 cm; BD= 10 cm ; CE= 10 cm.​

Answer 1

Como AB é paralelo a DE e os ângulos ACB e DCE são iguais, podemos afirmar que os triângulos ABC e CDE são semelhantes.

Sendo assim, podemos montar relações entre suas medidas, acompanhe:

$\frac{AC}{CD}~=~\frac{BC}{CE}\\\\\\\frac{2,5}{10}~=~\frac{x}{10}\\\\\\Multiplicando~Cruzado\\\\\\10~.~x~=~2,5~.~10\\\\\\10x~=~25\\\\\\x~=~\frac{25}{10}\\\\\\\boxed{x~=~2,5\,cm}$

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$\frac{AB}{DE}~=~\frac{AC}{CE}\\\\\\\frac{1,5}{y}~=~\frac{2,5}{10}\\\\\\Multiplicano~Cruzado\\\\\\2,5~.~y~=~1,5~.~10\\\\\\2,5y~=~15\\\\\\y~=~\frac{15}{2,5}\\\\\\\boxed{y~=~6\,cm}$