Question

determine as medidas de x e y indicadas nas figuras abaixo sabendo que r// s // t // u​

Answer 1

Utilizando o teorema de Tales podemos achar relações entre as medidas dos segmentos, acompanhe:

a)

$\boxed{\frac{6}{9}~=~\frac{10}{y}}\\\\\\6~.~y~=~9~.~10\\\\\\6y~=~90\\\\\\y~=~\frac{90}{6}\\\\\\\boxed{y~=~15}\\\\\\\\\boxed{\frac{10}{y}~=~\frac{x}{21}}\\\\\\y~.~x~=~10~.~21\\\\\\15~.~x~=~210\\\\\\x~=~\frac{210}{15}\\\\\\\boxed{x~=~14}$

b)

$\boxed{\frac{7,5}{y}~=~\frac{3}{5}}\\\\\\3~.~y~=~7,5~.~5\\\\\\y~=~\frac{37,5}{3}\\\\\\\boxed{y~=~12,5}\\\\\\\\\boxed{\frac{7,5}{y}~=~\frac{x}{10+5}}\\\\\\y~.~x~=~7,5~.~15\\\\\\12,5~.~x~=~112,5\\\\\\x~=~\frac{112,5}{12,5}\\\\\\\boxed{x~=~9}$

Answer 2

A) 6/9 = 10/y

*multiplica-se cruzado*

6y=9.10

6y=90

y= 90/6

y=15

10/15=x/21

15x=10.21

15x= 210

X= 15/210

X= 14

Espero ter ajudado :)