Question

Nos triângulos abaixo, determine as medidas dos segmentos indicados:

Answer 1

Semelhança de triangulos.

b) Pares de lados semelhantes:

AM e AB , AN e AC , MN e BC

$\frac{AM}{AB}=\frac{AN}{AC}\\\\\frac{3x-1}{3x-1\;+\;4x+2}=\frac{4}{4+6}\\\\\frac{3x-1}{7x+1}=\frac{4}{10}\\\\(3x-1)*10=(7x+1)*4\\\\30x-10=28x+4\\\\2x=14\\\\x=\frac{14}{2}\\\\x=7$

Assim:

AM = 3*7-1 = 20

MB = 4*7+2 = 30

AB = AM + MB = 20+30 = 50

d)

Pares semelhantes:

BE e AB , ED e AC , BD e BC

$\frac{BE}{AB}=\frac{BD}{BC}\\\\\frac{x}{21}=\frac{10}{10+5}\\\\\frac{x}{21}=\frac{10}{15}\\\\15*x=10*21\\\\15x=210\\\\x=\frac{210}{15}\\\\x=14$

Assim:

y+x = 21

y + 14 = 21

y = 21 - 14

y = 7