Triangles ABC and DBC are right angled triangles with common hypotenuse BC. BD and AC intersect at P when produced. If PA = 8 cm, PC = 4 cm and PD = 3.2 cm, then the length of BD, in cm, is:

6.8

\(\Delta \)ABP and \(\Delta \)DCP are similar.

\(\frac{PA}{PD}\) = \(\frac{PB}{PC}\)

= PA x PC = PB x PD

= 8 x 4 = 3.2 x PB

= 32 = 3.2 x PB

= \(\frac{32}{3.2}\) = PB

= PB = 10

So,

BD = PB - PD

= 10 - 3.2 = 6.8

Therefore, BD is 6.8 cm.