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:
Answer & explanation
Correct answer: option 2
\(\Delta \)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.