Question

a planta abaixo nos mostra três terrenos cujas as laterais são paralelas.calcule em metros, As medidas x ,y e z indicadas

Answer 1

De acordo com a figura, podemos tirar as seguintes proporções:

$\dfrac{x}{20}=\dfrac{y}{30}=\dfrac{z}{50}~~~~~~\mathbf{(i)}$


Vamos escrever $y$ e $z$ em função de $x:$

$\bullet\;\;\dfrac{x}{20}=\dfrac{y}{30}\\\\\\ y=\dfrac{30x}{20}\\\\\\ y=\dfrac{3x}{2}~~~~~~\mathbf{(i)}$


$\bullet\;\;\dfrac{x}{20}=\dfrac{z}{50}\\\\\\ z=\dfrac{50x}{20}\\\\\\ z=\dfrac{5x}{2}~~~~~~\mathbf{(ii)}$

__________

A lateral mede 80 m. Portanto, devemos ter

$x+y+z=80\\\\ x+\dfrac{3x}{2}+\dfrac{5x}{2}=80\\\\\\ \dfrac{2x}{2}+\dfrac{3x}{2}+\dfrac{5x}{2}=80\\\\\\ \dfrac{2x+3x+5x}{2}=80\\\\\\ \dfrac{10x}{2}=80\\\\\\ 10x=2\cdot 80\\\\ 10x=160\\\\ \boxed{\begin{array}{c}x=16\mathrm{~m}\end{array}}$


Logo,

$y=\dfrac{3\cdot 16}{2}\\\\\\ y=\dfrac{48}{2}\\\\\\ \boxed{\begin{array}{c}y=24\mathrm{~m}\end{array}}$


$z=\dfrac{5\cdot 16}{2}\\\\\\ z=\dfrac{80}{2}\\\\\\ \boxed{\begin{array}{c}z=40\mathrm{~m}\end{array}}$


Bons estudos! :-)

Answer 2

Resposta:

resposta do classrrom

1) d 10 metros

2) b 16m, 24m e 40 m