Question

calcule o valor de x e y nos triangulos

Answer 1

Semelhança de triangulos.

a)

Os pares de lados semelhantes são: AD e AB, AE e EC, DE e BC

$\frac{AD}{AB}=\frac{AE}{AC}\\\\\frac{6}{6+9}=\frac{x}{15}\\\\6*15 = 15*x\\\\x=\frac{90}{15}\\\\x=6cm$

$\frac{AD}{AB}=\frac{DE}{BC}\\\\\frac{6}{6+9}=\frac{y}{18}\\\\6*18 = 15*y\\\\y=\frac{108}{15}\\\\x=7,2cm$

b) Os pares de lados semelhantes são: AB e BE, BD e BC, DE e AC

$\frac{AC}{DE}=\frac{BC}{BD}\\\\\frac{x}{7}=\frac{27}{9}\\\\7*27 = 9*x\\\\x=\frac{189}{9}\\\\x=21cm$

$\frac{AB}{BE}=\frac{BC}{BD}\\\\\frac{y}{8}=\frac{27}{9}\\\\8*27 = 9*y\\\\y=\frac{216}{9}\\\\x=24cm$

Answer 2

usando a semelhança de triângulos teremos:
y/18=6/15
y/18=6/15
15y=18*6
y=108/15

x/(x-15)=6/15
15x=6*(x-15)
15x=6x-90
6x-15x=-90
-9x=-90
x=90/9
x=10

b)
x/9=27/8
8x=27*9
x=243/8


y/7=27/8
8y=7*27
8y=189
y=189/8

espero ter ajudado