Question

Qual o valor de x? ...............................

Answer 1

Achando a hipotenusa dos triângulos retângulos menores:

$a^{2}=3^{2}+3^{2}\\a^{2}=2\cdot3^{2}\\a=\sqrt{2\cdot3^{2}}\\a=3\sqrt{2}$
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Achando a hipotenusa do triângulo retângulo grande:

$(hip)^{2}=12^{2}+14^{2}\\(hip)^{2}=144+196\\(hip)^{2}=340\\(hip)^{2}=4\cdot85\\hip=\sqrt{4\cdot85}\\hip=2\sqrt{85}$

A hipotenusa desse triângulo é a soma de x com as duas hipotenusas dos triângulos menores:

$hip=x+2\cdot a\\2\sqrt{85}=x+2\cdot3\sqrt{2}\\2\sqrt{85}=x+6\sqrt{2}\\x=2\sqrt{85}-6\sqrt{2}\\\\\boxed{\boxed{x=2(\sqrt{85}-3\sqrt{2})}}$