SOLUTION: In the diagram below, ABCG is a parallelogram. Line BF=40 cm and Line FE=16 cm. Find the length of Line ED Diagram: https://imgur.com/a/LdjdTqc

We draw CE and AD to create trapezoids (trapeziums if you live in the UK) 
ABCE and ABCD, so that we may use a well-known theorem, which is:

THEOREM: Trapezoid (trapezium) diagonals divide each other in the same ratio.

[The theorem is easily proved by similar triangles.]



In trapezoid ABCE, since the diagonals AC and BE divide each other in the same
ratio,



The two trapezoids share a common diagonal AC

In trapezoid ABCD, since the diagonals AC and BD divide each other in the same
ratio,















Answer = 84 cm.

Edwin

Triangles BFC and RFA are similar with the similarity coefficient of   = .

It implies that AE is    of BC,  or  EG is    of BC.

Hence, triangles DEG and DBC are similar with the similarity coefficient  .

THEREFORE,   = ,  or   = .

It implies   = ,  or


    5*DE = 3*(DE + 56)

    5*DE = 3*DE + 3*56

    5*DE - 3*DE = 3*56

        2*DE    = 3*56

          DE    = 3*56/2 = 3*28 = 84.


ANSWER.  DE = 84 units.