10. There are three right-angled triangles containing a 
$30^{\circ}$ angle, they are of different sizes, 
but they have one side equal. Then, in the order of the areas of these three triangles from largest to smallest, the ratio of their hypotenuses is
10. $2: \frac{2 \sqrt{3}}{3}: 1$.

Let the shorter leg of Triangle A equal the longer leg of Triangle B equal the hypotenuse of Triangle C. Then the hypotenuses of Triangles A, B, and C are $2$, $\frac{2 \sqrt{3}}{3}$, and $1$, respectively, i.e., the required ratio is $2: \frac{2 \sqrt{3}}{3}: 1$.