Question

Pelo teorema de pitagoras temos o valor de x igual a:

Answer 1

$\displaystyle \left(\frac{x}{2}\right)^2+x^2=(3\sqrt{5})^2\\\\\frac{x^2}{2^2}+x^2=9.5\\\\\frac{x^2}{4}+x^2=45\\\\\frac{x^2+4x^2}{4}=45\\\\\frac{5x^2}{4}=45\\\\5x^2=45.4\\5x^2=180\\\\x^2=\frac{180}{5}\\\\x^2=36\\x=\sqrt{36}\\x=6$

Alternativa C.

Answer 2

$\large \boxed{ \begin{array}{l} \sf (3 \sqrt{5}) {}^{2} = \begin{pmatrix} \sf\dfrac{x}{2} \end{pmatrix} {}^{2} + x { }^{2} \\ \\ \sf 9 \times 5 = \dfrac{x {}^{2} }{4} + x {}^{2} \\ \\ \sf 45 = \dfrac{5}{4}x {}^{2} \\ \\ \sf 36 =x {}^{2} \\ \\ \sf x {}^{2} = 36 \\ \\ \sf x = \sqrt{36} \\ \\ \boxed{ \boxed{ \sf{x = 6}}}\end{array}}$