Question

Calcule x em cada triângulo retângulo:​

Answer 1

Podemos utilizar as relações métricas do triangulo retângulo.

Obs.: Estarei chamando de "h" o outro vértice do lado de medida 2,4.

Vamos começar determinando o valor do lado BC.

$AB^{\,2}~=~Bh\times BC\\\\\\4^2~=~2,4\times BC\\\\\\BC~=~\frac{16}{2,4}\\\\\\BC~=~\frac{16}{\frac{24}{10}}\\\\\\BC~=~\frac{16\,.\,10}{24}\\\\\\\boxed{BC~=~\frac{20}{3}}$

Agora, utilizando o teorema de Pitágoras, podemos determinar valor de "x":

$BC^{\,2}~=~AB^{\,2}~+~AC^{\,2}\\\\\\\left(\frac{20}{3}\right)^2~=~4^2~+~x^2\\\\\\x^2~=~\frac{400}{9}~-~16\\\\\\x^2~=~\frac{256}{9}\\\\\\x~=~\sqrt{\frac{256}{9}}\\\\\\\boxed{x~=~\frac{16}{3}}$