Question

Resolva usando pitagoras: a hipotenusa é 3√3---os outros lados são 2x e 3x. Calcule.

Answer 1

$Resolu\c{c}\~ao \to \left\{\begin{array}{ccc}(hipotenusa)^2 = (cateto_1)^2+(cateto_2)^2\\\\(3\sqrt{3})^2 = (2x)^2+(3x)^2\\\\9*3 = 4x^2+9x^2\\\\27 = 13x^2\\\\\frac{27}{13} = x^2\\\\\sqrt{\frac{27}{13} }=x\\\\\frac{\sqrt{27}}{\sqrt{13}} = x\\\\\frac{\sqrt{27}*\sqrt{13}}{\sqrt{13}*\sqrt{13}}=x\\\\\frac{3\sqrt{3}*\sqrt{13}}{13} = x\\\\\boxed{\boxed{x = \frac{3\sqrt{39}}{13} \approx 1,441...}}\end{array}\right$

Espero ter ajudado. =^.^=

Answer 2

a² = b² + c²                  a = hipotenusa    b = cateto    c = cateto

(3√3)² = (2x)² + (3x)²

9 . 3 = 4x² + 9x²

27 = 13x² 

x² = 27/13

x = √(27/13)  = √2,0769 = 1,44