In figure, DE ||

From the figure,

AB = AD + DB

14cm = 8cm + BD

BD = 6cm

Now, let EC = xcm

Then, AE + EC = 7cm

AE + x = 7cm

AE = (7 – x)cm

Given: DE || BC, therefore by basic proportionality theorem,

8x = 6(7 – x)

8x = 42 – 6x

14x = 42

x

x = 3cm

AE = (7 – 3)cm = 4cm

Hence, the value of AE is 4cm.