Question

Determine o valor de x e y nos pares de triângulos semelhantes

Answer 1

Explicação passo-a-passo:

Como os triângulos são semelhantes, os lados correspondentes são proporcionais

I)

=> Valor de x

$\sf \dfrac{x}{4}=\dfrac{12}{8}$

$\sf 8x=4\cdot12$

$\sf 8x=48$

$\sf x=\dfrac{48}{8}$

$\sf \red{x=6}$

=> Valor de y

$\sf \dfrac{y}{8}=\dfrac{5}{4}$

$\sf 4y=8\cdot5$

$\sf 4y=40$

$\sf y=\dfrac{40}{4}$

$\sf \red{y=10}$

II)

=> Valor de x

$\sf \dfrac{x}{9}=\dfrac{6}{3}$

$\sf 3x=9\cdot6$

$\sf 3x=54$

$\sf x=\dfrac{54}{3}$

$\sf \red{x=18}$

=> Valor de y

$\sf \dfrac{y}{3}=\dfrac{12}{9}$

$\sf 9y=3\cdot12$

$\sf 9y=36$

$\sf y=\dfrac{36}{9}$

$\sf \red{y=4}$

e)

=> Valor de x

$\sf \dfrac{x}{6}=\dfrac{25}{30}$

$\sf 30x=6\cdot25$

$\sf 30x=150$

$\sf x=\dfrac{150}{30}$

$\sf \red{x=5}$

=> Valor de y

$\sf \dfrac{y}{6}=\dfrac{20}{30}$

$\sf 30y=6\cdot20$

$\sf 30y=120$

$\sf y=\dfrac{120}{30}$

$\sf \red{y=4}$

f)

=> Valor de x

$\sf \dfrac{x}{7}=\dfrac{12}{14}$

$\sf 14x=7\cdot12$

$\sf 14x=84$

$\sf x=\dfrac{84}{14}$

$\sf \red{x=6}$

=> Valor de y

$\sf \dfrac{y}{14}=\dfrac{8}{7}$

$\sf 7y=14\cdot8$

$\sf 7y=112$

$\sf y=\dfrac{112}{7}$

$\sf \red{y=16}$

g)

Pelo Teorema de Tales:

$\sf \dfrac{x}{6}=\dfrac{4}{4+8}$

$\sf \dfrac{x}{6}=\dfrac{4}{12}$

$\sf 12x=6\cdot4$

$\sf 12x=24$

$\sf x=\dfrac{24}{12}$

$\sf \red{x=2}$

h)

Pelo Teorema de Tales:

$\sf \dfrac{x}{10}=\dfrac{2}{2+3}$

$\sf \dfrac{x}{10}=\dfrac{2}{5}$

$\sf 5x=10\cdot2$

$\sf 5x=20$

$\sf x=\dfrac{20}{5}$

$\sf \red{x=4}$