Question

calcule x e y sabendo que a//b//c//d
por favor me ajudem​

Answer 1

Utilizando o Teorema de Tales, podemos montar relações entre as medidas dos segmentos apresentados.

a)

$\boxed{\frac{x}{8,4}~=~\frac{4}{5,6}}~~~~e~~~\boxed{\frac{4}{5,6}~=~\frac{9}{y}}\\\\\\Multiplicando~Cruzado~na~primeira~relacao:\\\\\\5,6~.~x~=~8,4~.~4\\\\\\5,6x~=~33,6\\\\\\x~=~\frac{33,6}{5,6}\\\\\\\boxed{x~=~6}\\\\\\Multiplicando~Cruzado~na~segunda~ralacao\\\\\\4~.~y~=~5,6~.~9\\\\\\4y~=~50,4\\\\\\y~=~\frac{50,4}{4}\\\\\\\boxed{y~=~12,6}$

b)

$\boxed{\frac{x}{25}~=~\frac{6}{5}}~~~~e~~~\boxed{\frac{6}{5}~=~\frac{16}{y}}\\\\\\Multiplicando~Cruzado~na~primeira~relacao:\\\\\\5~.~x~=~25~.~6\\\\\\5x~=~150\\\\\\x~=~\frac{150}{5}\\\\\\\boxed{x~=~30}\\\\\\Multiplicando~Cruzado~na~segunda~ralacao\\\\\\6~.~y~=~5~.~16\\\\\\6y~=~80\\\\\\y~=~\frac{80}{6}\\\\\\\boxed{y~=~\frac{40}{3}~\approx~13,33}$