Well, by the segment addition postulate, 3x + 5 + 5x - 7 = BD, so BD = 8x - 2.
Because you didn't include the instructions in the picture, I can't be sure if this is a rhombus or a rectangle, but if it is either, then 3x + 5 = 5x - 7, and x = 6
If this is true, then BD = 48 - 2 = 46, but only if the shape is either a rhombus or rectangle (or both would make it a square).
