Question 430495
If we let X and Y represent the two consecutive sides of the rectangle, then we have:

X2+Y2=(22)2

Since we're connecting midpoints, then the lengths of our adjacent sides are 1/2X and 1/2Y, respectively. Thus:
(1/2X)2+(1/2Y)2=1/4X2+1/4Y2.

If we divide our first equation by 4 we get:

1/4X2+1/4Y2=1/4 ((22)2)
"""""""=1/4(484)
"""""""=121

The line connecting the midpoints is the hypotenuse of the triangle formed by connecting said midpoints, which has a length of sq.rt.121, or 11.  Which is 1/2 of our original line.