ABCD is a rectangle. taking ad as a diameter ,a semicircle axd is drawn which intersects  the diagonal bd at X .if ab=12cm,ad=9cm then find the value of bd and bx

Join AX such that AX = DX -------- (1),
Angle AXD = 90° (angle in a semicircle)
angle XAD = angle ADX (From 1)
Now, in ∆AXD, by angle sum property, we get :-
angle XAD = angle ADX = 45°,
sin angle XAD = DX/AD,
45° = DX/AD,
1/√2 = DX/9
Therefore, DX = 9/√2 = BX (Because AX is perpendicular on BD)
Now, BD = DX + BX,
=9/√2 + 9/√2
=18/√2
=9/√2
=12.72 approximately.