Question

Calcule o valor dos elementos desconhecidos nos a triângulos retângulos.

Answer 1

Resposta:

a) x = 20

b) y = 6

Explicação passo-a-passo:

a) ∆ABC ~ ∆HAC ~ HBA

ou seja

AB ~ HA ~ HB

AC ~ HC ~ HA

BC ~ AC ~ AB

entao,

$\frac{HA}{HB} = \frac{HC}{HA}\\\\\frac{x}{16} = \frac{25}{x}\\\\\\x^{2} = 16 . 25\\\\x = \sqrt{16.25} \\\\x = \sqrt{16} . \sqrt{25}\\\\x = 4 . 5 \\\\x = 20$

b) analgamente a lera A temos

$\frac{HC}{AC} = \frac{AC}{BC}\\\\\frac{y}{12} = \frac{12}{24}\\\\2y = 12\\\\y = 6$