Answer: \(x=\sqrt{117}\)

Solution Method:  Using the Pythagorean Theorem:
    \begin{align*}
        9^2+6^2 &= x^2 \\
        81 + 36 &= x^2 \\
        117 &= x^2 \\
        \sqrt{117} &= x
    \end{align*}

Answer: 5

Solution Method: Let \(a=\sqrt{5}\) be the length of the shorter leg. Then the longer leg, \(b\) is \(2a\), or \(b=2\sqrt{5}\). Then we can solve for the hypotenuse, \(c\), using the Pythagorean Theorem. 
    \begin{align*}
        a^2+b^2 &= c^2 \\
        (\sqrt{5})^2 + (2\sqrt{5})^2 &= c^2 \\
        5 + (2^2) 5 &= c^2 \\
        5+ (4)5 &= c^2 \\
        5+20 &= c^2 \\
        25 &= c^2 \\
        \sqrt{25} &= \sqrt{c^2} \\
        5&=c
    \end{align*}