In a ΔABC, DE is parallel to BC, AD = 3 cm, AE = 4 cm and AC = 10 cm, then the value of BD in centimetres, is :

4.5 

 We know that,

If three angles of two triangles are equal then corresponding sides of similar triangles are proportional

We have,

In Δ ABC, AE = 4 cm

AD = 3 cm

AC = 10 cm 

\(\frac{ AD }{ AB }\) = \(\frac{ AE }{ AC }\)

= \(\frac{ 3 }{ AB }\) = \(\frac{ 4 }{ 10 }\)

= AB = 7.5 cm

As, AB = AD + BD

= 7.5 = 3 + BD

= BD = 4.5 cm