Rhombusted

The rhombus' area is just the sum of four congruent right triangles with side lengths $x$ and $\frac{3x-2}{2}$ , or:

$\frac{1}{2}(x)(\frac{3x-2}{2}) = 10 \Rightarrow 3x^2 - 2x - 40 = 0 \Rightarrow (3x+10)(x-4) = 0 \Rightarrow x = 4, -\frac{10}{3}$

of which we only admit the former positive value. The side lengths for one of these right triangles are $4$ and $\frac{3(4)-2}{2} = 5$ , which give the rhombus' side length (i.e. the hypothenuse) as $\sqrt{4^2 + 5^2} = \boxed{\sqrt{41}}.$