Question

Observe os segmentos de reta.
Sabendo que as igualdades a seguir são verdadeiras, determine o valor de X, Y e z.
Segue anexo.

Answer 1

Olá Alves.


Se trata de uma regra de 3 simples.

Organizando os dados e resolvendo a equação:

$\mathsf{CD=6}\\\mathsf{EF=4}\\\mathsf{IJ=9}\\\mathsf{AB=2x}\\\\\\\mathsf{\dfrac{CD}{EF}=\dfrac{IJ}{AB}}\\\\\\\mathsf{\dfrac{6}{4}=\dfrac{9}{2x}}\\\\\\\mathsf{2x\cdot 6=4\cdot 9}\\\\\mathsf{12x=36}\\\\\mathsf{x=\dfrac{36}{12}}\\\\\boxed{\mathsf{x=3}}$

Explicação:

Em regra de 3 simples você terá 2 frações igualadas, e terá que multiplicar o numerador de um pelo o denominador do outro e vice-versa.


$\mathsf{IJ=9}\\\mathsf{GH=2y-7}\\\mathsf{AB=2x}\\\mathsf{MN=2}\\\\\\\mathsf{\dfrac{9}{2y-7}=\dfrac{2x}{2}~~\gets~\boxed{\mathsf{x=3}}}\\\\\\\mathsf{\dfrac{9}{2y-7}=\dfrac{2\cdot3}{2}}\\\\\\\mathsf{\dfrac{9}{2y-7}=\dfrac{6}{2}}\\\\\\\mathsf{18=6\cdot(2y-7)}\\\\\mathsf{18=12y-42}\\\\\mathsf{18+42=12y}\\\\\mathsf{60=12y}\\\\\\\mathsf{y=\dfrac{60}{12}}\\\\\\\boxed{\mathsf{y=5}}$

$\mathsf{EF=4}\\\\\mathsf{KL=\dfrac{z}{2}-5}\\\\\mathsf{CD=6}\\\mathsf{IJ=9}\\\\\\\\\mathsf{\dfrac{4}{\dfrac{z}{2}-5}=\dfrac{6}{9}}\\\\\\\\\mathsf{4\cdot9=6\cdot\Big(\dfrac{z}{2}-5\Big)}\\\\\mathsf{36=\dfrac{6z}{2}-6\cdot5}\\\\\mathsf{36=3z-30}\\\\\mathsf{36+30=3z}\\\\\mathsf{66=3z}\\\\\mathsf{z=\dfrac{66}{3}}\\\\\boxed{\mathsf{z=22}}$


Dúvidas? comente.