Because in a right triangle, the midline of the hypotenuse is equal to half of the hypotenuse, and just two right triangles share the hypotenuse BC, the midline MD=MA, so the triangle MDA is an isosceles triangle.

And because n is the midpoint of AD, in an isosceles triangle, the midline of the bottom is perpendicular to the bottom, so MN⊥AD.

At RT△ABC, through calculation, the root number of BC=AB/cosABC=2 is 15, so MD= root number 15.

In the right triangle MND, DN= 1/2AD= root number 3, and Pythagorean theorem finds the root number 3 of MN=2.

So MN is twice as long as the root number 3.