Okay, here we have this:
Considering the provided figure, we are going to find the missing sides, so we obtain the following:
Then according to the altitude rule we obtain the following equality:
(1/3)/x = x/(1/6)
Let's solve for x:
x^2=(1/3)(1/6)
x^2=1/18
x=√(1/18)
x=1/√18
x=1/(3√2)
x=√2/6
Now let's find the other two missing sides using the Pythagorean theorem:
[tex]\begin{gathered} z=\sqrt{\left(\frac{1}{3}\right)^2+\left(\frac{\sqrt{2}}{6}\right)^2}^ \\ z=\sqrt{\lparen1/9)+\left(2/36\right)} \\ z=\sqrt{\left(1/9\right)+\left(1/18\right)} \\ z=\sqrt{\left(2/18\right)+\left(1/18\right)} \\ z=\sqrt{3/18} \\ z=\sqrt{1/6} \\ z=1/\sqrt{6} \end{gathered}[/tex]
Finally let's find y:
[tex]\begin{gathered} y=\sqrt{\left(1/6\right)^2+\left(\sqrt{2}/6\right)^2} \\ y=\sqrt{\left(1/36\right)+\left(2/36\right)} \\ y=\sqrt{3/36} \\ y=\sqrt{1/12} \\ y=1/\sqrt{12} \\ y=1/\left(2\sqrt{3}\right) \end{gathered}[/tex]