In ΔABD, C is the midpoint of BD. If AB = 10 cm, AD = 12 cm and AC = 9 cm, then BD = ?

Solution (By Examveda Team)

$$\eqalign{ & A{B^2} + A{D^2} = 2\left( {A{C^2} + B{C^2}} \right) \cr & 100 + 144 = 2\left( {81 + {x^2}} \right) \cr & \frac{{244}}{2} = 81 + {x^2} \cr & 122 - 81 = {x^2} \cr & {x^2} = 41 \cr & x = \sqrt {41} \cr & BD = 2\sqrt {41} \cr} $$