Question

Sendo DE//AB, determine X nos casos :​

Answer 1

letra A:

3+6/6=x/8

9/6=x/8

3/2=x/8

2x=8.(3)

2x=24

x=24/2

x=12

letra B:

36/27=x/x-10

12/9=x/x-10

4/3=x/x-10

3.x=4.(x-10)

3x=4x-40

3x-4x=-40

-x=-40

x=-40/-1

x=40

Answer 2

Como nos é garantido que o segmento DE é paralelo ao segmento BC (DE // BC), podemos afirmar que:

--> Em (a) e (b), os triângulos ABC e ADE são semelhantes.

Utilizando então semelhança de triângulos, temos:

a)

$\boxed{\dfrac{AB}{AD}~=~\dfrac{BC}{DE}}\\\\\\\\\frac{6+3}{6}~=~\frac{x}{8}\\\\\\\frac{9}{6}~=~\frac{x}{8}\\\\\\Multiplicando~Cruzado\\\\\\6~.~x~=~8~.~9\\\\\\x~=~\frac{72}{6}\\\\\\\boxed{x~=~12}$

b)

$\boxed{\dfrac{AD}{AB}~=~\dfrac{DE}{BC}}\\\\\\\\\frac{x}{x-10}~=~\frac{36}{27}\\\\\\Multiplicando~Cruzado\\\\\\27~.~x~=~36~.~(x-10)\\\\\\27x~=~36x~-~360\\\\\\-9x~=~-360\\\\\\x~=~\frac{-360}{-9}\\\\\\\boxed{x~=~40}$