In a ΔABC, a line DE is drawn from D point on AB to E point on AC such that DE∥BC. Also AD:DB is 2:5. If AC is 4.2cm, then what is the length of AE?

By Thales Theorem (Basic Proportionality Theorem), since DE∥BC in ΔABC:
EC
AE
​
=
DB
AD
​
=
5
2
​

This means that AE represents 2 parts out of a total of 2+5=7 parts of the line segment AC.

Given that the total length AC=4.2cm:

AE=
7
2
​
×AC
AE=
7
2
​
×4.2=2×0.6=1.2cm