Geometry

We can use the great pythaogrean theorem to our advantage. 

First off, let's set some variables. 

Let's let BC = a and AC = b. 

Now, using pythagoras, let's right some equations. We have

$\overline{AM} = \sqrt{b^2 + \left(\dfrac a2\right)^2} = \dfrac12 \sqrt{4b^2 + a^2}$ since AM is the median and we also have

$\overline{BN} = \sqrt{a^2+ \left(\dfrac{b}{2}\right)^2} = \dfrac12 \sqrt{4a^2 + b^2}$ since BN is also the median of the triangle. 

Now, we're trying to isolate a^2+b^2 because that's how we find the hypotenuse of the triangle. 

Thus, we now have

$4b^2 + a^2 = 2^2 \\4a^2 + b^2 = 2^2$

Now, adding the two equations up with each other and dividing both sides by 5, we find that

$a^2 + b^2 = \dfrac{4+4}{5} = 8/5$

So the hypotenuse is that square rooted, which is $\sqrt{\frac{8}{5}}$

So $\sqrt{\frac{8}{5}}$ is our final answer. 

Thanks! :)