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答案：A
解析：
We can see from the diagram that the bisector BD intersects AC at a right angle, so the segments are perpendicular to each other.
Any point on a segment's perpendicular bisector is equidistant from the segment's two endpoints. Labeling the congruent line segments yields the following figure:
](http://pic.kekenet.com/2017/0728/5271501205379.png "SAT官方每日一题附答案和解析[数学](2017年7月28日)")
To find the perimeter of quadrilateral AECD, add the lengths of each side.
16+16+8+8=48
The perimeter of quadrilateral AECD is 48cm.
