Answer
$4', 6'$
Work Step by Step
1. Let the sides be $x,y$, based on the given conditions, we can get:
$\begin{cases}\frac{x}{y}=\frac{2}{3} \\ x^2+y^2=52 \end{cases}$
2. The 1st equation gives $x=\frac{2y}{3} $, use it in the 2nd equation to get $(\frac{4}{9})y^2+y^2=52$ or $y^2=36$, thus $y=6$, finally, use the 1st equation to get $x=4$
3. We have the solution(s) as: $4', 6'$
