A right triangle has an area of 48cm^2, and one side that is twice as the other side. what is the hypotenuse of this triangle?
In any right triangle with leg of lengths $\displaystyle a~\&~b$ its area is $\displaystyle \dfrac{a\cdot b}{2}$.
In your triangle we know that $\displaystyle a=2b$ thus its area is just $\displaystyle b^2$.
We also know that $\displaystyle c^2=a^2+b^2$ where $\displaystyle c$ is the length of the hypotenuse.
You need to finish it off.