Line segment AB is parallel to line segment CD. AD intersects BC in E. If lengths of AE, BC and ED are 18cm, 13.6cm and 6cm, what is the length of EC?

Given that AB∥CD and lines AD and BC intersect at E.
Consider △AEB and △DEC:

∠AEB=∠DEC (Vertically opposite angles)

∠EAB=∠EDC (Alternate interior angles as AB∥CD)

Therefore, by AA similarity criterion:

△AEB∼△DEC
From the property of similar triangles, corresponding sides are in the same ratio:

ED
AE
​
=
EC
BE
​

Given lengths:

AE=18cm

ED=6cm

BC=13.6cm

Let EC=x. Since E lies on BC, BE=BC−EC=13.6−x.

Substitute these into the ratio:

6
18
​
=
x
13.6−x
​

3=
x
13.6−x
​

3x=13.6−x
4x=13.6
x=
4
13.6
​
=3.4cm
Thus, the length of EC is 3.4cm.