In a rectangular trapezoid, the diagonal drawn from the top of the obtuse angle is equal to the side.

In a rectangular trapezoid, the diagonal drawn from the top of the obtuse angle is equal to the side. Find the ratio of the midline of this trapezoid to its larger base.

Draw a perpendicular CK from an obtuse angle to the base of trapezoid AD. Triangle ACD is isosceles by condition. In this case, CK is the median of the triangle, and AK = KD. Since BA and CK are perpendicular to AD, ABCK is a rectangle and BC = AK. Hence AD = 2BC. In a trapezoid, the middle line is MN = (BC + AD) / 2 = 3 / 2BC. The desired ratio is MN / AD = 3 / 2BC / 2BC = 3/4.