Question

02) Determine x e y na figura, sabendo que MN // BC e marque a alternativa correta.
(A) x = 12 e y = 4
(B)x = 4 e y = 12
(C) x = 4 e y = 10
(D) x = 10 e y = 12

Answer 1

Resposta:

Os triângulos ABC e AMN são semelhantes

• $\sf \dfrac{x+8}{8}=\dfrac{24}{16}$

$\sf 16\cdot(x+8)=8\cdot24$

$\sf 16x+128=192$

$\sf 16x=192-128$

$\sf 16x=64$

$\sf x=\dfrac{64}{16}$

$\sf x=4$

• $\sf \dfrac{y+6}{y}=\dfrac{24}{16}$

$\sf 24y=16\cdot(y+6)$

$\sf 24y=16y+96$

$\sf 24y-16y=96$

$\sf 8y=96$

$\sf y=\dfrac{96}{8}$

$\sf y=12$

Letra B