Question

6. Considerando a figura abaixo, calcule o
valor da expressão x + y.​

Answer 1

Resposta:

O valor da expressão x + y é igual a 9√5

Explicação passo-a-passo:

Usando o Teorema de Pitágoras, temos:

$y^2=8^2+4^2\\\\y^2=64+16\\\\y^2=80\\\\y=\sqrt{80}\\\\y=\sqrt{16\;.\;5}\\\\y=\sqrt{16}\;.\;\sqrt{5}\\\\y=4\sqrt{5}$

$x^2=y^2+(3\sqrt{5})^2\\\\x^2=(4\sqrt{5})^2+(3\sqrt{5})^2\\\\x^2=4^2\;.\;(\sqrt{5})^2+3^2\;.\;(\sqrt{5})^2\\\\x^2=16\;.\;5+9\;.\;5\\\\x^2=(16+9)\;.\;5\\\\x^2=25\;.\;5\\\\x=\sqrt{25\;.\;5}\\\\x=\sqrt{25}\;.\;\sqrt{5}\\\\x=5\sqrt{5}$

Portanto,

$x+y=4\sqrt{5}+5\sqrt{5}\\\\x+y=(4+5)\sqrt{5}\\\\\boxed{\boxed{x+y=9\sqrt{5}}}$