Question

detemine o valor das incógnitas:
​

Answer 1

Utilizando o teorema de Tales, podemos achar relações para determinar "x" e "y", acompanhe:

a)

$\frac{2,5}{5}~=~\frac{x}{6}\\\\\\Multiplicando~Cruzado\\\\\\5~.~x~=~2,5~.~6\\\\\\5x~=~15\\\\\\x~=~\frac{15}{5}\\\\\\\boxed{x~=~3}\\\\--------------------\\\frac{6}{x}~=~\frac{14}{y}\\\\\\14~.~x~=~6~.~y\\\\\\14~.~3~=~6y\\\\\\y~=~\frac{42}{6}\\\\\\\boxed{y~=~7}$

b)

$\frac{10}{5}~=~\frac{4}{x}\\\\\\Multiplicando~Cruzado\\\\\\10~.~x~=~4~.~5\\\\\\10x~=~20\\\\\\x~=~\frac{20}{10}\\\\\\\boxed{x~=~2}\\\\--------------------\\\frac{x}{4}~=~\frac{y}{7}\\\\\\7~.~x~=~4~.~y\\\\\\7~.~2~=~4y\\\\\\y~=~\frac{14}{4}\\\\\\y~=~\frac{7}{2}\\\\\\\boxed{y~=~3,5}$