Question

Na figura seguinte, temos MN // BC . Calcule x + y.
a) 3
b) 6
c) 9
d) 12
e) 15

Answer 1

Explicação passo-a-passo:

Os triângulos ABC e AMN são semelhantes, pelo caso AA, logo seus lados são proporcionais

=> Valor de x

$\sf \dfrac{\overline{AB}}{\overline{AC}}=\dfrac{\overline{AM}}{\overline{AN}}$

$\sf \dfrac{x+4}{x+3+6}=\dfrac{4}{6}$

$\sf \dfrac{x+4}{x+9}=\dfrac{4}{6}$

$\sf 6\cdot(x+4)=4\cdot(x+9)$

$\sf 6x+24=4x+36$

$\sf 6x-4x=36-24$

$\sf 2x=12$

$\sf x=\dfrac{12}{2}$

$\sf \red{x=6}$

=> Valor de y

$\sf \dfrac{\overline{BC}}{\overline{AB}}=\dfrac{\overline{MN}}{\overline{AM}}$

$\sf \dfrac{7,5}{x+4}=\dfrac{y}{4}$

$\sf \dfrac{7,5}{6+4}=\dfrac{y}{4}$

$\sf \dfrac{7,5}{10}=\dfrac{y}{4}$

$\sf 10y=7,5\cdot4$

$\sf 10y=30$

$\sf y=\dfrac{30}{10}$

$\sf \red{y=3}$

Logo:

$\sf x+y=6+3$

$\sf \red{x+y=9}$

Letra C