4. You're right that the leg labeled [tex]x[/tex] occurs in a 1-to-2 ratio with the hypotenuse, but more to the point, it also occurs with the leg of length 10 in a 1-to-[tex]\sqrt3[/tex] ratio. In other words,
[tex]10=x\sqrt3\implies x=\dfrac{10}{\sqrt3}[/tex]
and so
[tex]2x=\dfrac{20}{\sqrt3}[/tex]
5. In this kind of triangle, the legs form a 1-to-[tex]\sqrt2[/tex] ratio with the hypotenuse, so it follows that [tex]x=2.1[/tex].
6. You have [tex]x[/tex] and [tex]x\sqrt3[/tex] mismatched. The larger leg in this kind of triangle has the [tex]\sqrt3[/tex] scaling factor. So in fact, [tex]x=25[/tex], which makes the larger leg [tex]x\sqrt3=25\sqrt3[/tex], and the hypotenuse would be [tex]2x=50[/tex].
