Let, a = 7 cm, b = 13 cm, c = 12 cm
∴ s = (a + b + c)/2 = (7 +13 +12)/2 = 32/2 = 16 cm
Area of △ABC = under root(√s(s -a) (s - b)(s -c))
= under root(√16(16 - 7)(16 - 13)(16 - 12)
= under root(√16 x 9 x 3 x 4 = 24√3 cm^{2}
Also, Area of △ABC = 1/2AC.BD
24√3 = 1/2 x 12 x BD ⇒ BD = (24√3 x 2)/12
= 4√3 cm